We can solve this problem by setting up a system of linear equations and solve for the variables. Let's denote:
M = Cost of a medium jersey
L = Cost of a large jersey
From the given information, we can set up the following two equations:
8M + 5L = 277.50 (1) --> This is from the information that 8 medium and 5 large jerseys cost $277.50
3M + 7L = 234.75 (2) --> This is from the information that 3 medium and 7 large jerseys cost $234.75
Let's multiply equation (1) by 3 and equation (2) by 8 to make the coefficients of M the same in both equations:
24M + 15L = 832.50 (3)
24M + 56L = 1878.00 (4)
Now, we can subtract equation (3) from equation (4) to find L:
41L = 1045.50
So, L = 1045.50 / 41 = $25.50
Substitute L = 25.50 in the first equation:
8M + 5 * 25.50 = 277.50
8M + 127.50 = 277.50
8M = 150
M = 150 / 8 = $18.75
So, the cost of a medium jersey is $18.75 and the cost of a large jersey is $25.50.
We are asked to find the cost for an order of 4 medium and 3 large jerseys:
4M + 3L = 4 * 18.75 + 3 * 25.50 = $75.00 + $76.50 = $151.50