Answer:
Ryan has 10 pennies and 13 nickels.
Explanation:
Let the number of pennies be p and the number of nickels be n.
We have two unknowns, the number of pennies and the number of nickels, so we need two equations. One equation will deal with the value of the coins. The other equation will deal with the number of coins.
Value of coins:
1 penny is worth $0.01; p pennies are worth 0.01p.
1 nickel is worth $0.05; n nickels are worth 0.05n.
The total amount the coins are worth is
0.01p + 0.05n
The coins are worth $0.75, so we have our first equation.
0.01p + 0.05n = 0.75 Equation 1
Number of coins:
He has p pennies.
The number of nickels is 3 more than the number of pennies.
Since the number of pennies is p, then the number of nickels is p + 3.
That gives us our second equation.
n = p + 3 Equation 2
System of equations:
Now we have a system of two equations in two unknowns:
0.01p + 0.05n = 0.75
n = p + 3
Since the second equation is already solved for n, we can use the substitution method.
Replace n in the first equation with p + 3.
0.01p + 0.05n = 0.75
0.01p + 0.05(p + 3) = 0.75
Distribute the 0.05
0.01p + 0.05p + 0.15 = 0.75
Combine like terms on the left side.
0.06p + 0.15 = 0.75
Subtract 0.15 from both sides.
0.06p = 0.6
Divide both sides by 0.06.
p = 0.6/0.06
p = 10
Now we substitute 10 for p in the second equation to find the value of n.
n = p + 3
n = 10 + 3
n = 13
He has 10 pennies and 13 nickels.
Check:
A) 13 - 10 = 3 He does have 3 more nickels than pennies.
B) $0.01(10) + $0.05(13) = $0.10 + $0.65 = $0.75
The number of coins and the value of the coins both check out, so our answer is correct.
Answer: Ryan has 10 pennies and 13 nickels.