A dish contains 13 coins, all nickels or quarters. If there is a total of $1.85 in the dish, how many nickels are there, and how many quarters are there?

Answer 1

Set up two equations, one for total number of coins and one for total number of $.

NUMBER OF COINS (n = nickels; q = quarters)

n + q = 13

NUMBER OF $

0.05n + 0.25q = 1.85

STEP 1: Multiply the $ equation by -4 on both sides which will give you a -q value

n + q = 13

(-4) 0.05n + 0.25q = 1.85 (-4)

n + q = 13

-0.2n - q = -7.4

STEP 2: Add top equation to bottom equation removing 'q'

n + q = 13

-0.2n - q = -7.4

0.8n = 5.6

STEP 3: Solve for n by dividing 0.8 on both sides

0.8n = 5.6

0.8 0.8

n = 7; There are 7 nickels.

STEP 4: Plug in 7 for 'n' in the first number of coins equation to solve for 'q'

n + q = 13

7 + q = 13

q = 6; There are 6 quarters.

STEP 5: Verify that n=7 and q=6 works for the second $ equation

0.05n + 0.25q = 1.85

0.05(7) + 0.25(6) = 1.85

0.35 + 1.50 = 1.85

1.85 = 1.85

The answer is 7 nickels and 6 quarters.

Let me know if you have additional questions.

-TutorB