Question

Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 80 coins with a value of $16.25 inside of the bank.

Answer 1

The equations

`x + y = 80`

`0.25x + 0.1y = 16.25`

The solution

55 dimes and 25 quarters

Explanation:

Given

Let

`x \to` quarters

`y \to` dimes

`Total = 80`

`Worth = \$16.25`

Required

Set up a system of equation to calculate the number of each coin

The total coin of 80 implies that:

`x + y = Total`

`x + y = 80`

A dime = $0.1

A quarter = $0.25

So, the worth of the coin is:

`0.25 * x + 0.1 * y = Worth`

`0.25x + 0.1y = 16.25`

So, the equations are:

`x + y = 80`

`0.25x + 0.1y = 16.25`

Next, solve for x and y

Multiply the second equation by 4

`0.25x + 0.1y = 16.25` by 4

`x + 0.4y = 65`

Subtract from
`x + y = 80`

`x- x + y - 0.4y = 80 - 65`

`0.6y = 15`

Solve for y

`y = 25`

We have:

`x + y = 80`

`x = 80 - y`

`x = 80 - 25`

`x = 55`

Hence, there are 55 dimes and 25 quarters