Mei Ling brought some money to the school fair. She first spent 3/8 of it on games. Then she spent 2/5 of the remaining money on snacks. She had $36 left. How much money did Mei Ling have at first? How much did she spend altogether?
Try it yourself · watch the animation →Draw the total money as 8 equal parts. After 3 parts are spent, 5 parts are left. Then split these 5 parts into the 2/5 spent and the final remainder.
Answer: At first 96 $; Spent altogether 60 $
Method: For remainder fraction problems, draw the model step by step: first a fraction of the whole, then a fraction of the remainder. Match the final remaining units to the given amount to find 1 unit.
80 $ — After spending 1/5, 4/5 was left. Then he spent 3/4 of the remainder, so the final amount left was 1/4 of the remainder. The final amount left was 1/4 × 4/5 = 1/5 of all the money. 1/5 = $16, so all the money = $16 × 5 = $80.
16 marbles — After giving away 3/10, 7/10 remained. Then he gave away 2/7 of the remainder, so 5/7 of the remainder was left. The final amount left was 5/7 × 7/10 = 1/2 of all the marbles. 1/2 = 40 marbles, so the total was 80 marbles. After giving to his brother, 7/10 × 80 = 56 marbles remained. He gave his friend 2/7 × 56 = 16 marbles.
18 stamps — On Monday, she pasted 1/4, so 3/4 remained. On Tuesday, she pasted 2/3 of the remainder, so 1/3 of the remainder was left. The final amount left was 1/3 × 3/4 = 1/4 of all the stamps. 1/4 = 18 stamps, so the total was 72 stamps. On Monday, she pasted 1/4 × 72 = 18 stamps. On Tuesday, she pasted 2/3 × 54 = 36 stamps. She pasted 36 − 18 = 18 more stamps on Tuesday than on Monday.
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