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

Answer:

10 dimes.

Step-by-step 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:

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

$n+7=171-3n$

$n+3n+7-7=171-7-3n+3n$

$4n=164$

$\frac{4n}{4}=\frac{164}{4}$

$n=41$

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:

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

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

$6.05-0.15d=4.55$

$6.05-6.05-0.15d=4.55-6.05$

$-0.15d=-1.5$

$\frac{-0.15d}{-0.15}=\frac{-1.5}{-0.15}$

$d=10$

Therefore, there are 10 dimes in the bank.