Question

3. A box contains 36 books and some toys. The ratio of the number of books to the number of toys is 4 : 5.

After some toys are given away, the ratio of the number of books to the number of toys becomes 12:11. Find:

(1) the initial number of toys in the box,

(2) the number of toys that are given away.

Answer 1

1. 45
2. 12

Explanation:

Given 36 books in a box with toys such that the books : toys ratio is 4 : 5, you want the initial number of toys and the number given away if the ratio becomes 12 : 11.

Ratios

The number of books remains constant at 36. We can rewrite the ratios so that each shows the correct number of books:

ratios are books : toys

before: 4 : 5 = 36 : 45 . . . . . . . multiply by 9

after: 12 : 11 = 36 : 33 . . . . . . . . multiply by 3

1. Initial Toys

Based on the above, we see the initial number of toys is 45.

2. Given away

The final number of toys is 33, so the number given away is ...

45 -33 = 12

12 toys were given away.

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