A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase?

Setup number of coins:

• Number of nickels = n
• Number of dimes = 2.5n
• Number of quarters = 5n

Setup value of coins:

• Value of nickels = 0.05n
• Value of dimes = 2.5 * 0.1n = 0.25n
• Value of quarters = 5 * 0.25n = 1.25n

Add them up:
0.05n + 0.25n + 1.25n = 24.80

Solve for n in the equation 0.05n + 0.25n + 1.25n = 24.80

Step 1: Group the n terms on the left hand side:
(0.05 + 0.25 + 1.25)n = 1.55n

Step 2: Form modified equation
1.55n = + 24.8

Step 3: Divide each side of the equation by 1.55
1.55n/1.55 = 24.80/1.55
n = 16

Source