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

Answer:

The equations

$x + y = 80$

$0.25x + 0.1y = 16.25$

The solution

55 dimes and 25 quarters

Step-by-step 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