The base of a percentage often has to be built before it can be used
6.RP.A.3
Generated variants — 12
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 59, 39, 35, 67 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 59 students.
- School B sent 39 students.
- School C sent 35 students.
- School D sent 67 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
19.5 percent of 200 is 39, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 78, 45, 69, 108 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 78 students.
- School B sent 45 students.
- School C sent 69 students.
- School D sent 108 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
15 percent of 300 is 45, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 20, 108, 53, 19 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 20 students.
- School B sent 108 students.
- School C sent 53 students.
- School D sent 19 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
54 percent of 200 is 108, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 36, 114, 79, 71 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 36 students.
- School B sent 114 students.
- School C sent 79 students.
- School D sent 71 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
38 percent of 300 is 114, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 102, 138, 72, 88 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 102 students.
- School B sent 138 students.
- School C sent 72 students.
- School D sent 88 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
34.5 percent of 400 is 138, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 144, 99, 22, 35 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 144 students.
- School B sent 99 students.
- School C sent 22 students.
- School D sent 35 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
33 percent of 300 is 99, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 144, 75, 138, 143 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 144 students.
- School B sent 75 students.
- School C sent 138 students.
- School D sent 143 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
15 percent of 500 is 75, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 22, 15, 107, 156 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 22 students.
- School B sent 15 students.
- School C sent 107 students.
- School D sent 156 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
5 percent of 300 is 15, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 149, 123, 26, 202 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 149 students.
- School B sent 123 students.
- School C sent 26 students.
- School D sent 202 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
24.6 percent of 500 is 123, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 22, 89, 116, 273 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 22 students.
- School B sent 89 students.
- School C sent 116 students.
- School D sent 273 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
17.8 percent of 500 is 89, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 58, 85, 36, 321 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 58 students.
- School B sent 85 students.
- School C sent 36 students.
- School D sent 321 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
17 percent of 500 is 85, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
The table shows how many students from each school took part in a sports meet. If one representative is chosen from all the students, what percent chance is there that the representative comes from school B?
| School | A | B | C | D |
|---|---|---|---|---|
| Students |
Show solution
1 · Understandwhat's really being asked
Four schools sent 54, 26, 94, 326 students. One representative is picked from all of them, and we want the percent chance of the pick being from school B.
Givens
- School A sent 54 students.
- School B sent 26 students.
- School C sent 94 students.
- School D sent 326 students.
Unknowns
- The percent chance the representative comes from school B.
Constraints
- Every student is equally likely to be chosen.
2 · Planchoose the strategy
#8 Analyze the Units
A percentage needs a whole, and the table does not print one. Total every column first; only then is school B's share a division worth doing.
3 · Execute3 carry out the plan
1Total all four schools
2Write B's share as a fraction
3Turn it into a percent
4 · Reviewdoes it hold up?
5.2 percent of 500 is 26, which is exactly school B's column -- so the percentage and the count agree.
Standardsmin grade 6
6.RP.A.3Use ratio and rate reasoning to solve problems — Building the whole from the table and taking a percentage of it.
Where next?
← Back to the problem: The base of a percentage often has to be built before it can be used