← A rate you are given can be a way to recover what is missing · Ratio, Rate and Percent

A rate you are given can be a way to recover what is missing · 12 practice problems

6.RP.A.26.RP.A.3

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 26

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $104$ people and Hyuntae's has $100$ . If the population per unit area in Hyuntae's village is $50$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 100 people at 50 per square kilometre. Eunwoo's has 104 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 100 people, 50 per square kilometre.
Eunwoo's village: 104 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

50 people per square kilometre and 100 people in all.

100 \div 50 = 2

Hyuntae's village is 2 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

2 + 2 = 4

4 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

104 \div 4 = 26

26 people per square kilometre.

Answer: 26

4 · Reviewdoes it hold up?

26 people per square kilometre over 4 square kilometres gives 104 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 2 easy answer: 28

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $112$ people and Hyuntae's has $80$ . If the population per unit area in Hyuntae's village is $40$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 80 people at 40 per square kilometre. Eunwoo's has 112 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 80 people, 40 per square kilometre.
Eunwoo's village: 112 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

40 people per square kilometre and 80 people in all.

80 \div 40 = 2

Hyuntae's village is 2 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

2 + 2 = 4

4 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

112 \div 4 = 28

28 people per square kilometre.

Answer: 28

4 · Reviewdoes it hold up?

28 people per square kilometre over 4 square kilometres gives 112 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 3 easy answer: 30

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $120$ people and Hyuntae's has $80$ . If the population per unit area in Hyuntae's village is $40$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 80 people at 40 per square kilometre. Eunwoo's has 120 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 80 people, 40 per square kilometre.
Eunwoo's village: 120 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

40 people per square kilometre and 80 people in all.

80 \div 40 = 2

Hyuntae's village is 2 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

2 + 2 = 4

4 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

120 \div 4 = 30

30 people per square kilometre.

Answer: 30

4 · Reviewdoes it hold up?

30 people per square kilometre over 4 square kilometres gives 120 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 4 easy answer: 36

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $144$ people and Hyuntae's has $80$ . If the population per unit area in Hyuntae's village is $40$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 80 people at 40 per square kilometre. Eunwoo's has 144 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 80 people, 40 per square kilometre.
Eunwoo's village: 144 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

40 people per square kilometre and 80 people in all.

80 \div 40 = 2

Hyuntae's village is 2 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

2 + 2 = 4

4 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

144 \div 4 = 36

36 people per square kilometre.

Answer: 36

4 · Reviewdoes it hold up?

36 people per square kilometre over 4 square kilometres gives 144 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 5 medium answer: 65

Eunwoo's village is $1\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $195$ people and Hyuntae's has $160$ . If the population per unit area in Hyuntae's village is $80$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 160 people at 80 per square kilometre. Eunwoo's has 195 people and is 1 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 160 people, 80 per square kilometre.
Eunwoo's village: 195 people.
Eunwoo's village is 1 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

80 people per square kilometre and 160 people in all.

160 \div 80 = 2

Hyuntae's village is 2 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 1 square kilometres larger.

2 + 1 = 3

3 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

195 \div 3 = 65

65 people per square kilometre.

Answer: 65

4 · Reviewdoes it hold up?

65 people per square kilometre over 3 square kilometres gives 195 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 6 medium answer: 40

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $200$ people and Hyuntae's has $180$ . If the population per unit area in Hyuntae's village is $60$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 180 people at 60 per square kilometre. Eunwoo's has 200 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 180 people, 60 per square kilometre.
Eunwoo's village: 200 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

60 people per square kilometre and 180 people in all.

180 \div 60 = 3

Hyuntae's village is 3 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

3 + 2 = 5

5 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

200 \div 5 = 40

40 people per square kilometre.

Answer: 40

4 · Reviewdoes it hold up?

40 people per square kilometre over 5 square kilometres gives 200 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 7 medium answer: 35

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $245$ people and Hyuntae's has $200$ . If the population per unit area in Hyuntae's village is $40$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 200 people at 40 per square kilometre. Eunwoo's has 245 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 200 people, 40 per square kilometre.
Eunwoo's village: 245 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

40 people per square kilometre and 200 people in all.

200 \div 40 = 5

Hyuntae's village is 5 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

5 + 2 = 7

7 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

245 \div 7 = 35

35 people per square kilometre.

Answer: 35

4 · Reviewdoes it hold up?

35 people per square kilometre over 7 square kilometres gives 245 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 8 hard answer: 32

Eunwoo's village is $3\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $256$ people and Hyuntae's has $250$ . If the population per unit area in Hyuntae's village is $50$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 250 people at 50 per square kilometre. Eunwoo's has 256 people and is 3 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 250 people, 50 per square kilometre.
Eunwoo's village: 256 people.
Eunwoo's village is 3 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

50 people per square kilometre and 250 people in all.

250 \div 50 = 5

Hyuntae's village is 5 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 3 square kilometres larger.

5 + 3 = 8

8 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

256 \div 8 = 32

32 people per square kilometre.

Answer: 32

4 · Reviewdoes it hold up?

32 people per square kilometre over 8 square kilometres gives 256 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 9 medium answer: 32

Eunwoo's village is $3\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $256$ people and Hyuntae's has $200$ . If the population per unit area in Hyuntae's village is $40$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 200 people at 40 per square kilometre. Eunwoo's has 256 people and is 3 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 200 people, 40 per square kilometre.
Eunwoo's village: 256 people.
Eunwoo's village is 3 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

40 people per square kilometre and 200 people in all.

200 \div 40 = 5

Hyuntae's village is 5 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 3 square kilometres larger.

5 + 3 = 8

8 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

256 \div 8 = 32

32 people per square kilometre.

Answer: 32

4 · Reviewdoes it hold up?

32 people per square kilometre over 8 square kilometres gives 256 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 10 hard answer: 37

Eunwoo's village is $3\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $259$ people and Hyuntae's has $200$ . If the population per unit area in Hyuntae's village is $50$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 200 people at 50 per square kilometre. Eunwoo's has 259 people and is 3 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 200 people, 50 per square kilometre.
Eunwoo's village: 259 people.
Eunwoo's village is 3 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

50 people per square kilometre and 200 people in all.

200 \div 50 = 4

Hyuntae's village is 4 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 3 square kilometres larger.

4 + 3 = 7

7 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

259 \div 7 = 37

37 people per square kilometre.

Answer: 37

4 · Reviewdoes it hold up?

37 people per square kilometre over 7 square kilometres gives 259 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 11 hard answer: 39

Eunwoo's village is $3\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $273$ people and Hyuntae's has $160$ . If the population per unit area in Hyuntae's village is $40$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 160 people at 40 per square kilometre. Eunwoo's has 273 people and is 3 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 160 people, 40 per square kilometre.
Eunwoo's village: 273 people.
Eunwoo's village is 3 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

40 people per square kilometre and 160 people in all.

160 \div 40 = 4

Hyuntae's village is 4 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 3 square kilometres larger.

4 + 3 = 7

7 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

273 \div 7 = 39

39 people per square kilometre.

Answer: 39

4 · Reviewdoes it hold up?

39 people per square kilometre over 7 square kilometres gives 273 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.

Variant 12 hard answer: 39

Eunwoo's village is $2\ \text{km}^2$ larger in area than Hyuntae's. Eunwoo's village has $273$ people and Hyuntae's has $250$ . If the population per unit area in Hyuntae's village is $50$ , find the population per unit area in Eunwoo's.

Show solution

1 · Understandwhat's really being asked

Hyuntae's village has 250 people at 50 per square kilometre. Eunwoo's has 273 people and is 2 square kilometres bigger. We want Eunwoo's population per unit area.

Givens

Hyuntae's village: 250 people, 50 per square kilometre.
Eunwoo's village: 273 people.
Eunwoo's village is 2 square kilometres larger.

Unknowns

The population per unit area in Eunwoo's village.

Constraints

Neither village's area is given directly.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #11 Work Backwards#7 Identify Subproblems

Density needs an area, and no area is given. The density we do have is the way in: run it backwards to recover Hyuntae's area, add the difference, and only then divide.

3 · Execute3 carry out the plan

1Recover Hyuntae's area

#11 Work Backwards 6.RP.A.2

50 people per square kilometre and 250 people in all.

250 \div 50 = 5

Hyuntae's village is 5 square kilometres.

2Get Eunwoo's area

#7 Identify Subproblems 6.RP.A.3

It is 2 square kilometres larger.

5 + 2 = 7

7 square kilometres.

3Divide people by area

#8 Analyze the Units 6.RP.A.2

That is what population per unit area means.

273 \div 7 = 39

39 people per square kilometre.

Answer: 39

4 · Reviewdoes it hold up?

39 people per square kilometre over 7 square kilometres gives 273 people, which is Eunwoo's village exactly.

Another way: Comparing the two villages' populations alone would say Eunwoo's is busier, but it is also bigger -- and it is the area that decides which village is more crowded.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading population per unit area as a rate, in both directions.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Carrying the area difference through to the second density.

💡Takeaway. A rate works both ways. If you know how many per unit, you can get back to how many units.