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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.

Respuesta :

MrRoyal

Answer:

The equations

[tex]x + y = 80[/tex]

[tex]0.25x + 0.1y = 16.25[/tex]

The solution

55 dimes and 25 quarters

Step-by-step explanation:

Given

Let

[tex]x \to[/tex] quarters

[tex]y \to[/tex] dimes

[tex]Total = 80[/tex]

[tex]Worth = \$16.25[/tex]

Required

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

The total coin of 80 implies that:

[tex]x + y = Total[/tex]

[tex]x + y = 80[/tex]

A dime = $0.1

A quarter = $0.25

So, the worth of the coin is:

[tex]0.25 * x + 0.1 * y = Worth[/tex]

[tex]0.25x + 0.1y = 16.25[/tex]

So, the equations are:

[tex]x + y = 80[/tex]

[tex]0.25x + 0.1y = 16.25[/tex]

Next, solve for x and y

Multiply the second equation by 4

[tex]0.25x + 0.1y = 16.25[/tex] by 4

[tex]x + 0.4y = 65[/tex]

Subtract from [tex]x + y = 80[/tex]

[tex]x- x + y - 0.4y = 80 - 65[/tex]

[tex]0.6y = 15[/tex]

Solve for y

[tex]y = 25[/tex]

We have:

[tex]x + y = 80[/tex]

[tex]x = 80 - y[/tex]

[tex]x = 80 - 25[/tex]

[tex]x = 55[/tex]

Hence, there are 55 dimes and 25 quarters

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