# A jar contains $10.75 in dimes and quarters. If the number of dimes is four more than twice the number of quarters, determine the number of each type of coin.

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### 2 Answers

Let quarters be represented by the variable "x".

Then dimes would be represented by 2x + 4.

The value of a quarter is 0.25 therefore, the total money for quarters can be represented by `0.25x.`

The value of a dime is 0.10 therefore the total value of dimes can be represented by `0.10(2x + 4)` .

The total can be found adding the 2 values together to equal $10.75.

`.25x + .10(2x + 4) = 10.75` Solve for x

`0.25x + 0.2x + .4 = 10.75`

`0.45x = 10.35`

`x = 23`

**Therefore, there are 23 quarters and 50 dimes.**

A jar contains $10.75 in dimes and quarters. The number of dimes is four more than twice the number of quarters.

Let x represent the number of quarters in the jar.

As the number of dimes is 4 more than twice the number of quarters, it can be represented by 2x + 4

Now the value of dimes is .1*(2x+4) and the value of quarters is 0.25*x

.1*(2x+4) + 0.25*x = 10.75

.2*x + .4 + .25*x = 10.75

0.45*x = 10.35

x = 23

This gives the number of quarters in the jar as 23 and the number of dimes is 50.