Question

Janet has a jar of 54 coins consisting of dimes and quarters. If she has a total of $8.70, how many dimes does she have?

Answer 1

you need 2 equations with 2 unknowns

let d = dimes and q = quarters

then

d + q = 54 (1) number of coins
0.1d + 0.25q = 8.70 (2) value of the coins

substitution method is probably the easiest

rewrite equation (1)

q = 54 - d

substitute into equation 2

0.1d + 0.25(54 - d) = 8.70

expand and collect like terms

0.1d + 13.5 - 0.25d = 8.70

-0.15d + 13.50 = 8.70

-0.15d = - 4.80

d = 32

the container holds 32 dimes

no substitute into equation (1) to find the quarters

32 + q = 54

q = 22

checking

0.1 x 32 + 0.25 x 22 = 3.20 + 5.50
= 8.70