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.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

the olimpics is not going to wokk out

step-by-step explanation: