Harlan has $44 to buy 7 pairs of socks. Athletic socks cost $5 per pair. Dress socks cost $8 per pair. Write a system of equations for this situation, use the elimination method to solve the system, then answer the questions below. Use "x" and "y" as your variables.
Let x represent the number of athletic socks Harlan buys
Let y represent the number of dress socks Harlan buys
The first equation is: x + y = 7 (since Harlan buys 7 pairs of socks)
The second equation is: 5x + 8y = 44 (since he has $44)
To solve the system of equations by elimination we will begin by multiplying the first equation by -8 to eliminate the y variable:
-8(x + y) = -8(7)
-8x - 8y = -56
Now we can add this new equation to the second equation:
-8x - 8y + 5x + 8y = -56 + 44
-3x = -12
Now we can solve for x:
-3x = -12
x = -12 / -3
x = 4
So, Harlan buys 4 pairs of athletic socks.
We can substitute this value of x into one of the original equations to solve for y:
4 + y = 7
y = 7 - 4
y = 3
So, Harlan buys 3 pairs of dress socks.
Therefore, Harlan buys 4 pairs of athletic socks and 3 pairs of dress socks.