Question

Yolanda paid for her movie ticket using 28 coins all nickles and quarters. The ticket cost $4. Which system of linear equations can be used to find the number of nickles,n, and the number of quarter,q, Yolanda used?

Answer 1

The number of nickels are 15 and the numbers of quarters are 13 .

Explanation:

As given

The number of nickles = n

The number of quarter be q

As given

Yolanda paid for her movie ticket using 28 coins all nickles and quarters.

Than the equations becomes

n + q = 28

As given the ticket cost $4.

As

1 quarter = 0.25 dollar

1 nickel = 0.05 dollar

Than the equation becomes

0.05n + 0.25q = 4

Simplify the above

`(5n)/(100) + (25q)/(100) = 4`

5n + 25q = 400

Than two equations are

n + q = 28 and 5n + 25q = 400

Multiply n + q = 28 by 5 and subtracted from 5n + 25q = 400 .

5n - 5n + 25q - 5q = 400 - 140

20q = 260

`q = (260)/(20)`

q = 13

Put in the equation n + q = 28

n + 13 = 28

n = 28 - 13

n = 15

Therefore the number of nickels are 15 and the numbers of quarters are 13 .