Question

A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is

$16.65. Find the number of each coin using SUBSTITUTION.

Answer 1

The number of nickels is 45 and the number of dimes is 72.

Explanation:

Let

x ----> number of nickels

y ----> number of dimes

Remember that

`1\ nickel=\$0.05`

`1\ dime=\$0.10`

so

`0.05x+0.10y=9.45` ------> equation A

`0.05x+0.10(2y)=16.65`

`0.05x+0.20y=16.65` ------> equation B

Solve the system by substitution

we have

`0.05x+0.10y=9.45` ------> equation A

`0.05x+0.20y=16.65` ------> equation B

Multiply both equations by 100 both sides

`5x+10y=945` ---->
`5x=945-10y` --> equation C

`5x+20y=1,665` ----> equation D

substitute equation C in equation D

`(945-10y)+20y=1,665`

solve for y

`945+10y=1,665`

`10y=1,665-945`

`10y=720`

`y=72\ dimes`

Find the value of x

`5x=945-10y`

`5x=945-10(72)`

`5x=225`

`x=45\ nickels`

Alternative Method

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is the point (45,72)

therefore

The number of nickels is 45 and the number of dimes is 72.