Math question Algebra need help

Question

Michael has a jar full of dimes and quarters. There are a total of 120 coins with a total value of $19.20. The system of equations below represents this situation.

How many MORE dimes than quarters are in Michael's jar?

A.12

B.15

C.24

D.48

Answer 1

Hi Neha,

The system of equations we want to solve is the following:

(1) x + y = 120

(2) 25x + 10y = 1920

if x is the number of quarters and y is the number of dimes. We want to find y-x, how many more dimes there are than quarters.

Notice that, from (1) y = 120 - x. Substitute this into (2) to obtain:

25x + 10(120 - x) = 1920

which implies that:

25x + 1200 - 10x = 1920

15x + 1200 = 1920

15x = 720

x = 48.

Then using equation (1) again we have

y = 120 - 48 = 72.

So our answer is y - x = 72 - 48 = 24.

So the answer is C.

Let me know if you need more help. Maybe we can schedule a lesson!