Question

Kirsten has 25 coins. In her collection she has dimes and quarters. If the total is $4.00. How many dimes and how many quarters does she have?

Write a system of equations to express this situation. Let d = the number of dimes and Let q = the number of quarters.

Solve the system of equations to determine the number of dimes and the number of quarters.

Answer 1

System of equations:
d + q = 25
10d + 25q = 400

From first equation find d:
d = 25 - q

Then replace it in second​ equation:
10(25 - q) + 25q = 400
250 - 10q + 25q = 400
250 + 15q = 400
15q = 400 - 250
15q = 150
q = 150 / 15 = 10

Now replace q in first equation with found value:
d + 10 = 25
d = 25 - 10 = 15

So, Kirsten has 15 dimes and 10 quarters.

Answer 2

q would equal 10 and d would equal 15. You use the elimination method using the equations 25q+10d=400 (25 and 10 because those are the values of the coins and the equation d+q=25. d and q equal the total amount of coins.