Question

Michael's bank contains only nickels, dimes, and quarters. There are 57 coins in all, valued at $4.55. The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank

Answer 1

10 dimes.

Explanation:

Let n represent number of nickels, d represent number of dimes and q represent number of quarters.

We have been given that there are 57 coins in all. We can represent this information in an equation as:

`n+d+q=57...(1)`

We are also told that the value of all coins is $4.55. We can represent this information in an equation as:

`0.05n+0.10d+0.25q=4.55...(2)`

The number of nickels is 7 short of being three times the sum of the number of dimes and quarters together. We can represent this information in an equation as:

`n+7=3(d+q)...(3)`

From equation (1), we will get:

`d+q=57-n`

Substituting this value in equation (3), we will get:

`n+7=3(57-n)`

`n+7=171-3n`

`n+3n+7-7=171-7-3n+3n`

`4n=164`

`(4n)/(4)=(164)/(4)`

`n=41`

Therefore, there are 41 nickels in the bank.

`d+q=57-n...(1)`

`d+q=57-41...(1)`

`d+q=16...(1)`

`q=16-d...(1)`

Upon substituting equation (1) and value of n in equation (2), we will get:

`0.05(41)+0.10d+0.25(16-d)=4.55`

`2.05+0.10d+4-0.25d=4.55`

`6.05-0.15d=4.55`

`6.05-6.05-0.15d=4.55-6.05`

`-0.15d=-1.5`

`(-0.15d)/(-0.15)=(-1.5)/(-0.15)`

`d=10`

Therefore, there are 10 dimes in the bank.