michael's bank contains only nickels, dimes, and quarters. there are 64 coins in all, valued at $5.30. the number of nickels is 8 short of being three times the sum of the number of dimes and quarters together. how many dimes are in the bank?

Number of dims in the bank are 10.                  

Step-by-step explanation:

Given : Michael's bank contains only nickels, dimes, and quarters. There are 64 coins in all, valued at $5.30. The number of nickels is 8 short of being three times the sum of the number of dimes and quarters together.

To find : How many dimes are in the bank?

Solution :

Let number of nickels = x

Number of dims = y

Number of quarters = z

Total there are 64 coins.

i.e. ....(1)

The cost of nickels = $0.05

The cost of dims = $0.10

The cost of quarters = $0.25

Total value at $5.30.

i.e. .....(2)

The number of nickels is 8 short of being three times the sum of the number of dimes and quarters together.

i.e. .....(3)

Substitute y+z from (1),

Substitute the value of x in (1) and (2),

.....(4)

 .....(5)

Solving equation (4) and (5),

Substitute the value of y from (4) in (5),

Substitute the value of z in (4),

So, Number of nickels are x=46

Number of dims are y=10

Number of quarters are z=8.

Therefore, Number of dims in the bank are 10.