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cody has 3.20 in his piggy bank made up of nickels dimes and quarters. there are 3 times as many quarters as nickles and 5 more dimes than nickles. how many coins of each does he have?

9 Quarters

8 Dimes

3 Nickels

Step-by-step explanation:

We let the number of quarters be q

number of dimes be d

and

number of nickels be n

Since quarters are worth 0.25, dimes are worth 0.10 and nickels are worth 0.05 and total worth is 3.20, we can write an equation as:

0.25q + 0.10d + 0.05n = 3.20

Next,

3 times as many quarters as Nickels, we can write:

q = 3n

and

5 more dimes than nickel, we can write:

d = n + 5

Substituting these last 2 equations in the first and solving for n gives us:

0.25q + 0.10d + 0.05n = 3.20

0.25(3n) + 0.10(n+5) + 0.05n = 3.20

0.75n + 0.10n +0.5 + 0.05n = 3.20

0.9n = 2.70

n = 2.70/0.9 = 3

n = 3

We know q = 3n, so

q = 3(3) = 9

Also, we know d = n + 5, which means:

d = 3 + 5 = 8

Thus,

There are:

9 Quarters

8 Dimes

3 Nickels

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