Question

A person has 28 coins, all dimes and quarters, worth $4.60. How many quarters are there?

16
18
12

Answer 1

12

Explanation:

D=dimes Q=quarters

D+Q=28 so D=28-Q

460=10D+25Q

substitute 28Q for D

10(28-Q)+25Q=460

280-10Q+25Q=460

combine like terms

15Q=180

divide both sides by 15 so Q= 12 and D=16

(I believe this is the correct answer)

Answer 2

Remember that a dime is worth 10 cents and a quarter is worth 25 cents and $4.60 is 460 cents.

Let D = the number of dimes and Q = the number of quarters.

Now let's translate the English into math. . .

there are 28 coins in all--> D + Q = 28 so D = 28 - Q

they are worth 460 cents--> 10D + 25Q = 460

Now substitute 28-Q for D--> 10(28-Q) + 25Q = 460

280 - 10Q + 25Q = 460

Combine like term. . .

15Q = 180

Divide both sides by 15--> Q = 12

So D = 16