Internal Transfer
Given: 1 Ratio, Total Amount, Amount of Change
Answer: One Side
First
Mike and Jake had 480 stamps.
After Mike had given 169 stamps to Jake, Jake had 3 times as many stamps as Mike.
How many stamps did Mike have at first?
After Mike had given 169 stamps to Jake, Jake had 3 times as many stamps as Mike.
How many stamps did Mike have at first?
(After)
Jake : Mike : Total
= 3 : 1 : 4
4u = 480
Mike = 1u = 120
(Before)
Mike = 120 + 169 = 289
Given: 1 Ratio, Total Amount, Amount of Change
Answer: Difference
First
Leon and his sister Lily have a total of 120 crayons. If Leon gives Lily 5 crayons, Lily will have nine times as many crayons as Leon. How many more crayons does Lily have than Leon?
(After)
Lily : Leon : Total : Difference
= 9 : 1 : 10 : 8
10u = 120
8u = 120 ÷ 5 × 4 = 96
(Before)
Difference = 96 + 2 × 5 = 106
Answer: One Side
First
Rick had 3 times as much money as Fiona. After Rick gave $285 to Fiona, he had twice as much money as she did. How much money did Rick have at first?
Ratio Method
(Equalise Total Units)
(Before)
Rick : Fiona : Total
= 3 : 1 : 4
= 9 : 3 : 12
(After)
Rick : Fiona : Total
= 2 : 1 : 3
= 8 : 4 : 12
1u = $285
(Before)
Rick = 9u = $2565
Fraction Method
(Find Common Denominator of Required Fraction)
(Before)
Rick = 3/4 = 9/12
(After)
Rick = 2/3 = 8/12
1u = $285
9u = $2565
Second
Class A had 1/3 the number of pupils in Class B. After 14 pupils were transferred from Class B to Class A, Class A had 4/5 the number of pupils in Class B. How many pupils were there in Class A at first?
Third
Shirley and Jimmy collected some stamps in the ratio 1 : 2. When Shirley received 35 stamps from Jimmy, the ratio of the number of Shirley`s stamps to Jimmy`s stamps became 4 : 3. How many stamps did they have altogether?
Multiple Transfers
Roger had twice as many marbles as Mark at first. Mark gave 1/2 of his marbles to Roger and Roger gave 3/5 of his marbles back to Mark. In the end, Mark had 8 more marbles than Roger. How many marbles did each of them have at first?
Common Denominator of Successive Changes
1/2 = 5/10
3/5 = 6/10
(Before)
Roger : Mark
= 2 : 1
= 20 : 10
10u × 1/2 = 5u
(After 1)
Roger : Mark
= 25 : 5
25u × 3/5 = 15u
(After 2)
Roger : Mark : Difference
= 10 : 20 : 10
10u = 8
(Before)
Mark = 10u = 8
Roger = 8 × 2 = 16
Given: Ratios of 2 Cases, Small to Big Transfers
First
Robin had 75% as many marbles as David. After Robin gave 72 marbles to David, David had four times as many marbles as Robin. How many marbles had Robin left?
75% = 3/4
(Before)
Robin : David : Total
= 3 : 4 : 7
= 15 : 20 : 35
(After)
Robin : David : Total
= 1 : 4 : 5
= 7 : 28 : 35
Change of Units = Small to Big Change
15 - 7 = 8 units
8 units = 72
Robin (After) = 7 units = 63
Given: Ratios of 2 Cases, Opposite Transfers
First
First
If Randolf gave Lynette $8, he would have the same amount of money as Lynette. If Lynette gave Randolf $8, the ratio of the amount of money she had to the amount of money Randolf had would be 1 : 2. How much money did each of them have?
Equalise Total Units Method
(Case 1)
Randolf : Lynette : Total
= 1 : 1 : 2
= 3 : 3 : 6
(Case 2)
Randolf : Lynette : Total
= 2 : 1 : 3
= 4 : 2 : 6
Change of Units = Sum of Opposite Changes
4 - 3 = 1 unit
1 unit = $8 + $8 = $16
Randolf = 3 units + $8 = $48 + $8 = $56
Lynette = 3 units - $8 = $48 - $8 = $40
Equalise Total Units Method
(Case 1)
Randolf : Lynette : Total
= 1 : 1 : 2
= 3 : 3 : 6
(Case 2)
Randolf : Lynette : Total
= 2 : 1 : 3
= 4 : 2 : 6
Change of Units = Sum of Opposite Changes
4 - 3 = 1 unit
1 unit = $8 + $8 = $16
Randolf = 3 units + $8 = $48 + $8 = $56
Lynette = 3 units - $8 = $48 - $8 = $40
Second
If Shirley gives Tanya 12 wristbands, she will have the same number of wristbands as Tanya. If Tanya gives Shirley 4 wristbands, the ratio of the number of wristbands she has to the number of wristbands Shirley has will be 3 : 5. How many wristbands does Tanya have?
If Shirley gives Tanya 12 wristbands, she will have the same number of wristbands as Tanya. If Tanya gives Shirley 4 wristbands, the ratio of the number of wristbands she has to the number of wristbands Shirley has will be 3 : 5. How many wristbands does Tanya have?
Third
If Kimberly gives Louis 15 game cards, she will have the same number of game cards as Louis. If Louis gives Kimberly 10 game cards, the ratio of the number of game cards he has to the number of game cards Kimberly has will be 2 : 7. How many game cards does Louis have?
If Kimberly gives Louis 15 game cards, she will have the same number of game cards as Louis. If Louis gives Kimberly 10 game cards, the ratio of the number of game cards he has to the number of game cards Kimberly has will be 2 : 7. How many game cards does Louis have?
Fourth
If Shop A transfers 38 mobile phone cases to Shop B, Shop A will have the same number of mobile phone cases as Shop B. If Shop B transfers 22 mobile phone cases to Shop A, the ratio of the number of mobile phone cases Shop B has to the number of mobile phone cases Shop A has will be 7 : 15. How many mobile phone cases does Shop A have?
If Shop A transfers 38 mobile phone cases to Shop B, Shop A will have the same number of mobile phone cases as Shop B. If Shop B transfers 22 mobile phone cases to Shop A, the ratio of the number of mobile phone cases Shop B has to the number of mobile phone cases Shop A has will be 7 : 15. How many mobile phone cases does Shop A have?
Fifth
If Kraig gives 18 marbles to Luke, he will have thrice as many marbles as Luke. If Luke gives 12 marbles to Kraig, he will have 1/9 of the number of marbles that Kraig has. How many marbles does Kraig have at first?
If Kraig gives 18 marbles to Luke, he will have thrice as many marbles as Luke. If Luke gives 12 marbles to Kraig, he will have 1/9 of the number of marbles that Kraig has. How many marbles does Kraig have at first?
Sixth
If Uncle Glenn gives Aunt Susie 12 cookies, he will have twice as many cookies as her. If Aunt Susie gives Uncle Glenn 8 cookies, Uncle Glenn will have 8 times as many cookies as her. How many cookies does Uncle Glenn have at first?
If Uncle Glenn gives Aunt Susie 12 cookies, he will have twice as many cookies as her. If Aunt Susie gives Uncle Glenn 8 cookies, Uncle Glenn will have 8 times as many cookies as her. How many cookies does Uncle Glenn have at first?
Seventh
If Joe gives 1 of his postcards to Fred, Fred will have 1/ 4 as many postcards as Joe. However, if Fred gives 13 of his postcards to Joe, Joe will have 9 times as many postcards as Fred. How many postcards does Fred have?
If Joe gives 1 of his postcards to Fred, Fred will have 1/ 4 as many postcards as Joe. However, if Fred gives 13 of his postcards to Joe, Joe will have 9 times as many postcards as Fred. How many postcards does Fred have?
Eighth
If Cindy gives 2 mini toys to Joey, Cindy will have 3 times as many mini toys as Joey. If Joey gives 16 mini toys to Cindy, the ratio of Joey's mini toys to Cindy's mini toys will be 1 : 7. How many mini toys does Joey have?
If Cindy gives 2 mini toys to Joey, Cindy will have 3 times as many mini toys as Joey. If Joey gives 16 mini toys to Cindy, the ratio of Joey's mini toys to Cindy's mini toys will be 1 : 7. How many mini toys does Joey have?
Ninth
Ali and Ben each have a sum of money.
If Ali gives $6.20 to Ben, he would have 1/5 of Ben's amount.
If Ben gives $12.80 to Ali, he would have 3 times as much money as Ali.
How much money does Ben have?
Ali and Ben each have a sum of money.
If Ali gives $6.20 to Ben, he would have 1/5 of Ben's amount.
If Ben gives $12.80 to Ali, he would have 3 times as much money as Ali.
How much money does Ben have?
(Case 1)
Ali : Ben : Total
= 1 : 5 : 6
= 2 : 10 : 12
= 1 : 5 : 6
= 2 : 10 : 12
(Case 2)
Ali : Ben : Total
= 1 : 3 : 4
= 3 : 9 : 12
Difference of Units = Sum of Opposite Changes
= 1 : 3 : 4
= 3 : 9 : 12
Difference of Units = Sum of Opposite Changes
3 - 2 = 1 unit
1 unit = $6.20 + $12.80 = $19
Ben = 10 units - $6.20
= $190 - $6.20 = $183.80
Tenth
Adam and Ben each have some money. If Adam spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 3:5. If Ben spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 11:13. How much money does each boy have?
= $190 - $6.20 = $183.80
Tenth
Adam and Ben each have some money. If Adam spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 3:5. If Ben spends $4, the ratio of the amount of money Adam has to the amount that Ben has will be 11:13. How much money does each boy have?
Eleventh
If Irvin gives Jess $7, he will have the same amount of money as Jess. If Jess gives Irvin $5, the ratio of the amount of money she has to the amount of money Irvin has will be 2 : 3. How much money does Jess have?
Given: Ratios of 2 Cases, Similar Transfers
FirstJames and Cain have some money, If James gives $16 to Cain. James will have 4 times as much money as Cain. If James gives $30 to Cain, the ratio of the amount of money James has to the amount of money Cain has will be 9 : 4. How much money do they have altogether?
(Case 1)
James : Cain : Total
= 4 : 1 : 5
= 52 : 13 : 65
(Case 2)
James : Cain : Total
= 9 : 4 : 13
= 45 : 20 : 65
Change of Units = Difference of Similar Changes
52 units - 45 units = 7 units
7 units = $30 - $16 = $14
Total = 65 units = $130
Sixth
52 units - 45 units = 7 units
7 units = $30 - $16 = $14
Total = 65 units = $130
Second
If a fruit-seller transfers 20 apples from Crate A to Crate B, Crate A will have 1 1/5 times as many apples as Crate B. If he transfers 97 apples from Crate A to Crate B, Crate A will have 1/3 as many apples as Crate B. How many apples are there in Crate A?
1 1/5 = 3/2
(Case 1)
Crate A : Crate B : Total
= 3 : 2 : 5
= 12 : 8 : 20
(Case 2)
Crate A : Crate B : Total
= 1 : 3 : 4
= 5 : 15 : 20
Change of Units = Difference of Similar Changes
12 units - 5 units = 7 units
7 units = 97 - 20 = 77
Crate A = 5 units + 97 = 55 + 97 = 152
If a fruit-seller transfers 20 apples from Crate A to Crate B, Crate A will have 1 1/5 times as many apples as Crate B. If he transfers 97 apples from Crate A to Crate B, Crate A will have 1/3 as many apples as Crate B. How many apples are there in Crate A?
1 1/5 = 3/2
(Case 1)
Crate A : Crate B : Total
= 3 : 2 : 5
= 12 : 8 : 20
(Case 2)
Crate A : Crate B : Total
= 1 : 3 : 4
= 5 : 15 : 20
Change of Units = Difference of Similar Changes
12 units - 5 units = 7 units
7 units = 97 - 20 = 77
Crate A = 5 units + 97 = 55 + 97 = 152
Third
There are children gathering in Hall X and Hall Y. If 52 children move from Hall X to Hall Y, the number of children in Hall X will be 7/8 of the number of children in Hall Y. If 73 children move from Hall X to Hall Y, then the number of children in Hall X will be 7/11 of the number of children in Hall Y. How many children are there in Hall Y?
There are children gathering in Hall X and Hall Y. If 52 children move from Hall X to Hall Y, the number of children in Hall X will be 7/8 of the number of children in Hall Y. If 73 children move from Hall X to Hall Y, then the number of children in Hall X will be 7/11 of the number of children in Hall Y. How many children are there in Hall Y?
Fourth
If Carol gives $140 to Dan, the ratio of her money to Dan will be 7 : 3. If Carol gives $550 to Dan, the ratio of her money to Dan's money will be 3: 13. How much money does Dan have?
Fifth
If Julie gives 10 clips to Maria, she will have 4 times as many clips as Maria. If Julie gives 34 clips to Maria, she will have twice as many clips as Maria. How many clips does Julie have?
If Carol gives $140 to Dan, the ratio of her money to Dan will be 7 : 3. If Carol gives $550 to Dan, the ratio of her money to Dan's money will be 3: 13. How much money does Dan have?
Fifth
If Julie gives 10 clips to Maria, she will have 4 times as many clips as Maria. If Julie gives 34 clips to Maria, she will have twice as many clips as Maria. How many clips does Julie have?
James and Cain have some money. If James gives S16 to Cain. James will have 4 times as much money as Cain. If James gives S30 to Cain, the ratio of the amount of money James has to the amount of money Cain has will be 9 : 4. How much money do they have altogether?
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