Anonymous

# can someone help me with this?

John and David each bought a certain number of toy cars from a shop. John gave1/5 of his toy cars to David. Then David gave 2/9 of what he had back to John. Next, John gave 1/4 of all his toy cars to David. In the end, John had 36 toy cars and David had 68 toy cars. How many toy cars did each of them buy from the shop at first?

Relevance

Or you can start from the end and work backwards.

After giving David 1/4 of what he had , John was left with 36 cars. That means 3/4 of what he originally had = 36. Thus he must have started with 36 * 4 / 3 = 48 cars.

Thus on the last go , John had 48 cars , out of which he gave 12 to David. After receiving the 12 from John , David ended up with 68 cars ; this means he must have started with 56 cars.

When he had 56 cars , it was after giving 2/9 of what he had , to John. This means 56 was 7/9 of what he had. Thus he started with 56 * 9 / 7 i.e. 72 cars. Out of this he gave 2/9 or 16 cars to John. Since after this transfer John had 48 cars , he started the second go with 32 cars.

Initially , John gave 1/5 of what he had to David. Which means 4/5 of what he started off with = 32. Thus at the beginning , John had 32 * 5 / 4 = 40 cars , out of which he gave David 8. Which means David started off with (72 - 8) = 64.

John has 40 toy cars at first

Davis has 64 toy cars at first

• Anonymous

1/5x - 2/9x - 1/4x =36

36 x 1/4 = 9

36 + 9 = 45

45 x 2/9 = 10

45 + 10 = 55

55 x 1/5 = 11

55 + 11 = 66