George has only Quarters and nickels in his piggy bank. He has a total of 90 coins. The value of the coins is $16.10. Write and solve a system that can be used to determined how many quarters and how many nickels he has.

The number of

Quarters = q = 58 quarters

Nickels = n = 32 nickels

Step-by-step explanation:

It is important to note that:

A quarter is worth 25 cents = 0.25q

A nickel is worth 5 cents = 0.05n

George has only Quarters and nickels in his piggy bank.

Let the number of

Quarters = q

Nickels = n

He has a total of 90 coins.

Hence,

q + n = 90 Equation 1

q = 90 - n

The value of the coins is $16.10.

Hence,

0.25q + 0.05n = 16.10Equation 2

We substitute 90 - n for q in Equation 2

0.25(90 - n) + 0.05n = 16.10

22.5 - 0.25n + 0.05n = 16.10

Collect like terms

- 0.25n + 0.05n = 16.10 - 22.5

-0.2n = - 6.4

n = -6.4/-0.2

n = 32 nickels

Solving for q

q = 90 - n

q = 90 - 32

q = 58 quarters

Therefore, the number of

Quarters = q = 58 quarters

Nickels = n = 32 nickels

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step-by-step explanation: