Respuesta :
Answer:
You find 19 nickels.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of nickels.
y is the number of dimes.
z is the number of quarters.
66 coins
This means that x + y + z = 66.
With a face value of $11.55.
Nickel is worth $0.05, dime worth $0.1 and quarter worth $0.25. So
0.05x + 0.1y + 0.25z = 11.55.
A coin dealer offers you $10 for each nickel, $20 for each dime, and $15 for each quarter, for a total of $945.
This means that 10x + 20y + 15z = 945.
How many nickels did you find?
We have to find x.
From the first equation:
z = 66 - x - y
Replacing in the second:
0.05x + 0.1y + 0.25z = 11.55.
0.05x + 0.1y + 0.25(66 - x - y) = 11.55
0.05x + 0.1y + 16.5 - 0.25x - 0.25y = 11.55
0.2x + 0.15y = 4.95
So
0.15y = 4.95 - 0.2x
y = 33 - 1.33x
On the final equation:
10x + 20y + 15z = 945
10x + 20(33 - 1.33x) + 15(66 - x - (33 - 1.33x)) = 945
10x + 660 - 26.6x + 15(66 - x - 33 + 1.33x) = 945
-16x + 660 + 15(33 + 0.33x) = 945
-16x + 660 + 495 + 5x = 945
11x = 210
x = 210/11
x = 19
You find 19 nickels.
