Sharing in a ratio cuts the whole into as many parts as the terms add to
7.RP.A.36.RP.A.3
Generated variants — 12
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $80 and $120 and share a profit of $60 in that ratio. We want the first one's share.
Givens
- Emma invested $80 and Noah $120.
- The profit is $60.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $24 and $36, add to $60 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $90 and $150 and share a profit of $40 in that ratio. We want the first one's share.
Givens
- Emma invested $90 and Noah $150.
- The profit is $40.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $15 and $25, add to $40 -- the whole profit -- and stand in the ratio 3 to 5.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $120 and $180 and share a profit of $50 in that ratio. We want the first one's share.
Givens
- Emma invested $120 and Noah $180.
- The profit is $50.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $20 and $30, add to $50 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $150 and $200 and share a profit of $70 in that ratio. We want the first one's share.
Givens
- Emma invested $150 and Noah $200.
- The profit is $70.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $30 and $40, add to $70 -- the whole profit -- and stand in the ratio 3 to 4.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $160 and $240 and share a profit of $100 in that ratio. We want the first one's share.
Givens
- Emma invested $160 and Noah $240.
- The profit is $100.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $40 and $60, add to $100 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $250 and $150 and share a profit of $80 in that ratio. We want the first one's share.
Givens
- Emma invested $250 and Noah $150.
- The profit is $80.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $50 and $30, add to $80 -- the whole profit -- and stand in the ratio 5 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $180 and $270 and share a profit of $150 in that ratio. We want the first one's share.
Givens
- Emma invested $180 and Noah $270.
- The profit is $150.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $60 and $90, add to $150 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $210 and $280 and share a profit of $70 in that ratio. We want the first one's share.
Givens
- Emma invested $210 and Noah $280.
- The profit is $70.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $30 and $40, add to $70 -- the whole profit -- and stand in the ratio 3 to 4.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $240 and $360 and share a profit of $90 in that ratio. We want the first one's share.
Givens
- Emma invested $240 and Noah $360.
- The profit is $90.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $36 and $54, add to $90 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $300 and $450 and share a profit of $75 in that ratio. We want the first one's share.
Givens
- Emma invested $300 and Noah $450.
- The profit is $75.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $30 and $45, add to $75 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $500 and $300 and share a profit of $160 in that ratio. We want the first one's share.
Givens
- Emma invested $500 and Noah $300.
- The profit is $160.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $100 and $60, add to $160 -- the whole profit -- and stand in the ratio 5 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
Emma invested and Noah invested , and they will split the profit in the ratio of what they invested. If the total profit is , how much does Emma get?
Show solution
1 · Understandwhat's really being asked
Two people put in $400 and $600 and share a profit of $250 in that ratio. We want the first one's share.
Givens
- Emma invested $400 and Noah $600.
- The profit is $250.
- The profit is split in the ratio of the investments.
Unknowns
- Emma's share of the profit.
Constraints
- The two shares together are the whole profit.
2 · Planchoose the strategy
#7 Identify Subproblems
Simplify the ratio before doing anything with it, then add its terms: that sum is how many equal pieces the profit is cut into, which is the number the division needs.
3 · Execute4 carry out the plan
1Simplify the ratio of the investments
2Count the pieces
3Find one piece
4Give Emma her share
4 · Reviewdoes it hold up?
The two shares, $100 and $150, add to $250 -- the whole profit -- and stand in the ratio 2 to 3.
Standardsmin grade 7
7.RP.A.3Use proportional relationships to solve multi-step ratio and percent problems — Dividing a total in a given ratio.6.RP.A.3Use ratio and rate reasoning to solve problems — Simplifying the ratio of the two investments.
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