Question posted by Sandy from the United States:

Grade/Level: 5th Grade

Question: Joe and Moe were on the bus last Monday when a sneaky pickpocket stole some of their money. They went back home and counted their money. Joe had $91 more than Moe so he gave Moe 2/5 of his money. Joe had 6/7 as much money as Moe after that. How much money did Joe have before he gave Moe some?

Answer:

Step 1: This question involves the Constant Total Concept. For this question, it is easier to work backwards as there is a "Multiples Relationship" between the before and after model(i.e. Joe had 6/7 as much money as Moe after that.). We draw 6 boxes to represent the total amount of money Joe had and 7 boxes to represent the amount of money Moe had after the transfer.

Step 2: If Joe gave 2/5 of his money to Moe, then he must have 3/5 of his money left. So we mark the remaining 6 units of Joe's money as 3/5.

Step 3: Working backwards, we will now "transfer" the 2/5 given to Moe back to Joe. Since 3/5 is equivalent to 6 unit, then 2/5 must be equivalent to 4 units. we draw this 4 units in dotted lines as they do not belong to Joe now.

Step 4: We were also told in the question that Joe had $91 more than Moe. Before the transfer, Joe should have 10 units and Moe 3 units. So we mark the difference between their money, i.e. 10 units - 3 units = 7 units as $91.

From the model,

7 units ---------- $91

1 unit ---------- $91 / 7 = $13

10 units ---------- 10 x $13 = $130

Therefore, Joe had $130 before he gave Moe some money.

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