Question

Has 44 coins;quarters and nickels. The combined value of the coins is $7. How many quarters and nickels does he have?

Answer 1

The number of nickel's coin is 20 and the number of quarter's coin is 24

Explanation:

Let

x ----> the number of nickel's coin

y ----> the number of quarter's coin

Remember that

`1\ nickel=\$0.05`

`1\ quarter=\$0.25`

so

we have

`x+y=44`

`x=44-y` ----> equation A

`0.05x+0.25y=7` ----> equation B

Solve the system by substitution

substitute equation A in equation B

`0.05(44-y)+0.25y=7`

solve for y

`2.2-0.05y+0.25y=7`

`0.20y=7-2.2`

`0.20y=4.8`

`y=24`

Find the value of x

`x=44-24=20`

therefore

The number of nickel's coin is 20 and the number of quarter's coin is 24