Question

Mark had 3 times as many quarters as nickels. He had $1.60 in all. How many nickels and how many quarters did Mark have?

Answer 1

See a solution process below:

Explanation:

First, let call:
- `q` the number of quarters Mark had
- `n` the number of nickels Mark had

From the information in the problem we can write two equations:

• Equation 1: `q = 3n`

• Equation 2: `$0.25q + $0.05n = $1.60`

Step 1) Because Equation 1 is solved for `q` we can substitute `(3n)` for `q` in Equation 2 and solve for `n`:

`$0.25q + $0.05n = $1.60` becomes:

`$0.25(3n) + $0.05n = $1.60`

`$0.75n + $0.05n = $1.60`

`($0.75 + $0.05)n = $1.60`

`$0.80n = $1.60`

`($0.80n)/(color(red)($)color(red)(0.80)) = ($1.60)/(color(red)($)color(red)(0.80))`

`(color(red)(cancel(color(black)($0.80)))n)/cancel(color(red)($)color(red)(0.80)) = (color(red)(cancel(color(black)($)))1.60)/(cancel(color(red)($))color(red)(0.80))`

`n = 1.60/color(red)(0.80)`

`n = 2`

Step 2) Substitute `2` for `n` in the Equation 1 and calculate `q`:

`q = 3n` becomes:

`q = 3 xx 2`

`q = 6`

The Solution Is:

• Mark has 6 quarters
• Mark has 2 nickels