Answer:
The number of
Quarters = q = 58 quarters
Nickels = n = 32 nickels
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 = 16.10....Equation 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