Question 230553: Carlos has some pennies, nickels, and quarters in his pocket. He has 2 more nickels than quarters. He has twice as many pennies as nickels. The total value is $1.74. How many of each coin does Carlos have?
Answer by likaaka(51)   (Show Source):
You can put this solution on YOUR website! First begin by naming your variables.
Let P be the amount, not worth, of pennies Carlos has, N will be the amount of nickels, and Q the amount of quarters.
So if Carlos has 2 more nickels than quarters, your first equation is
N = Q + 2
If he has twice as many pennies as nickels, then
P = 2N
Now we use the value of each coin to determine the third equation.
0.01P + 0.05N + 0.25Q = 1.74
Here's your system of equations
N = Q + 2
P = 2N
0.01P + 0.05N + 0.25Q = 1.74
I would start be rearranging the first equation so that it's solved for Q
N = Q + 2 becomes Q = N - 2 by subtracting 2 from both sides
Now substitute the value of Q and the value of P into the third equation to solve for N
0.01(2N) + 0.05N + 0.25(N-2) = 1.74, distribute
0.02N + 0.05N + 0.25N - 0.5 = 1.74, combine like terms
0.32N - 0.5 = 1.74, add 0.5 to both sides
0.32N = 2.24, divide both sides by 0.32
N = 7, so Carlos has 7 nickels
Given Q = N - 2 and N = 7 solve for Q
Q = 7 - 2
Q = 5, so Carlos has 5 quarters
Given P = 2N and N = 7
P = 2(7)
P = 14, so Carlos has 14 pennies
CHECK:
0.01(14) + 0.05(7) + 0.25(5) = 1.74
0.14 + 0.35 + 1.25 = 1.74
1.74 = 1.74
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