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

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