The currency called the dollar can be divided or reduced into smaller forms also known as pennies, quarters, nickels and dimes.
The number of pennies is 5, the number of dimes is 5, the number of quarters is 30.
It is important to note that
a penny = $0.01
a dime = $0.10
a quarter = $0.25
Let's represent the number of
pennies = p
dimes = d
quarters = q
The number of pennies is equal to the number of dimes, hence:
p = q, so we can represent the number of pennies and dimes as y
The box currently contains 40 coins
So: 40 = y + y + q
q = 40 - 2y...........Equation 1
The total value of the coins is $8.05
So: 0.01y + 0.1y + 0.25q = 8.05 ........... Equation 2
We substitute 40 - 2y for q in Equation 2
0.01y + 0.1y + 0.25(40 - 2y) = 8.05
0.01y + 0.1y + 10 - 0.5y = 8.05
Collect like terms
0.01y + 0.1y - 0.5y = 8.05 - 10
-0.39y = -1.95
Divide both sides by -0.39
-0.39y/-0.39 = -1.95/0.39
y = 5
Since y represents the number of pennies and dimes, the number of pennies is 5 and the number of quarters is 5.
To solve for the number quarters, we would use equation 1
q = 40 - 2y...........Equation 1
q = 40 - 2 x 5
q = 40 - 10
q = 30
The number of quarters is 30.
Therefore, we have 5 pennies, 5 dimes, and 30 quarters.
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