Question

In a pile of coins, there are 7 quarters than nickels. If there is a total of 2.65 in coins, how many total coins are there? How many of each type of coin is in the pile?

Answer 1

In the pile there are 10 quarters and 3 nickels.

Explanation:

Given:

Total amount of money = $2.65

Let number of nickels be 'n'.

Also Let number of quarters be 'd'

Now we now that;

nickels 'n' =$0.05

Quarters 'q' = $0.25

So the equation can be framed as;

`0.05n+0.25q = 2.65 \ \ \ \ equation\ 1`

Now Given:

there are 7 more quarters than nickels.

So we can say that;

`q=n+7 \ \ \ equation 2`

Now Substituting equation 2 in equation 1 we get;

`0.05n+0.25q = 2.65\\\\0.05n+ 0.25(n+7) =2.65\\\\0.05n+0.25n+1.75= 2.65\\\\0.3n+1.75 =2.65`

Now Subtracting both side by 1.75 using subtraction property of equality we get;

`0.3n+1.75-1.75=2.65-1.75\\\\0.3n = 0.9`

Now Dividing both side by 0.3 using division property of Inequality we get;

`(0.3n)/(0.3)=(0.9)/(0.3)\\\\n = 3`

Now Substituting the value of n in equation 2 we get;

`q=n+7 = 3+7 =10`

Hence In the pile there are 10 quarters and 3 nickels.