Question

A bag contains 23 coins, some dimes and some quarters. The total amount of money in the bag is $2.75. How many dimes and how many quarters are

in the bag?

X dimes

X quarters

Answer 1

Step-by-step explanation:

A bag contains 23 coins, some dimes and some quarters. The total amount of money in the bag is $2.75.

Let d be the  number of dimes

and q be the number of quarters

Total cons = 23

so equation becomes

$d+q= 23$

$q=23-d$

1 dime = 10 cents

and 1 quarter =25 cents

The total amount of money in the bag is $2.75

2.75= 275 cents

$10d+25q=275$

solve the equation for d  and q

Plug in $q=23-d$ for q in second equation

$10d+25q=275\\10d+25(23-d)=275\\10d+575-25d=275$

combine like terms and subtract 575 from both sides

$10d+575-25d=275\\-15d=275-575\\-15d=-300$

divide both sides by -15

d=20

so the number of dimes = 20

$q=23-d\\q=23-20\\q=3$

Number of quarter = 3

Answer:

20 dimes

3 quarters