Question posted by YC Mak from Singapore:

Grade/Level: 6th Grade

Question solved by Model Method: Andy bought a watch for $540. He gave 1/5 of the remainder to his brother bought a earphone for $180 and finally have 1/14 of money left. How much money did Andy have at beginning?

Answer:

Step 1: This question involves the Remainder Concept. We first draw 1 long bar to represent the total amount of money that Andy had at the beginning.

Step 2: Since Andy bought a watch for $540, we mark out 1 box to represent the $540 he spent on the watch.

Step 3: As he gave 1/5 of the remainder to his brother, we divide the remaining bar into 5 equal units and mark out 1 unit to represent the 1/5 of the remainder given to the brother.

Step 4: He then bought a earphone for $180, so we mark out an unknown part to represent $180 spent on the earphone.

Step 5: Then the remaining part must be equal to 1/14 of the remainder.

Step 6: From the model, we can see that

4 units ----------> $180 + 1/14

1 unit ----------> ($180 + 1/14) / 4 = $45 + 1/56

5 units ----------> 5 x ($45 + 1/56) = $225 + 5/56

We also noted that 1/14 = 4/56.

Step 7: Since the unknown portion of his money on the extreme right is 5/56 of the total he had at the beginning, then the other 2 parts on the left must be equal to 51/56 of the total amount of money he had at the beginning.

Thus, from the model, we can see that

51/56 ----------> $540 + $225 = $765

1/56 ----------> $765 / 51 = $15

56/56 ----------> 56 x $15 = $840

Therefore, Andy had $840 at the beginning.

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