Layla has $6.17 in change in her piggy bank. The change consists of 113 coins in a mix of pennies, nickels, and quarters. If there are 8 times as many nickels as pennies, how many of each coin does Layla have?
Write a system of linear equations that models this given problem scenario.

Using a system of equations, it is found that there are 12 pennies, 96 nickels and 5 quarters.

In the system of equations, I am going to say that:

There is a total of 113 coins, hence:

$6.17 in change, hence, considering the value of each coin:

8 times as many nickels as pennies, hence:

Replacing the third equation on the first two:

Then

Then

There are 12 pennies, 96 nickels and 5 quarters.

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There are 12 pennies, 96 nickels, and 5 quarters.

Step-by-step explanation:

Let x = number of pennies

y= number of nickels

z= number of quarters

As per given ,

Since 1 penny =1 cent

1 nickel = 5 cents

1 quarter = 25 cents

so, $6.17 = 617cents  [1 dollar = 100 cents]

Now,

Required system of linear equations:

Put value of y from (ii) in (i), we get

Use (ii) and (iv) in (iii), we get

from (ii), y= 8(12)=96

from (iv), z=113-9(12)=113-108=  5

hence, there are 12 pennies, 96 nickels, and 5 quarters.