Question

A bag of coins contains only quarters and dimes. The number of dimes in the bag can be represented by x. The number of quarters is 6 more than twice the number of dimes. There are a total of 276 coins in the bag. What is x, the number of dimes in the bag?

Answer 1

There are 90 coins in the bag.

Explanation:

Let
`x`,
`y` the number of dimes and quarters. Now we proceed to translate each relevant sentence into mathematical expressions:

(i) The number of quarters is 6 more than twice the number of dimes:

`y = 2\cdot x + 6` (1)

(ii) There are a total of 276 coins in the bag:

`x + y = 276` (2)

By applying (1) in (2), we find that the number of dimes is:

`x+2\cdot x + 6 = 276`

`3\cdot x = 270`

`x = 90`

There are 90 coins in the bag.