An event planner routinely orders ice sculptures for the corporate events she plans. For an executive dinner in Weston, she ordered 5 small ice sculptures and 3 large ice sculptures, which cost $813. Then, for a release party in Richmond, she ordered 5 small ice sculptures and 5 large ice sculptures, which cost a total of $1,055. How much does each ice sculpture cost?
Let the cost of a small ice sculpture be S and the cost of a large ice sculpture be L.
From the information given, we have the following equations:
5S + 3L = 813 (1)
5S + 5L = 1055 (2)
Multiply equation (1) by 5 to get:
25S + 15L = 4065 (3)
Subtract equation (2) from equation (3):
25S + 15L - (5S + 5L) = 4065 - 1055
20S + 10L = 3010 (4)
Divide both sides of equation (4) by 10:
2S + L = 301 (5)
Substitute equation (5) into equation (1):
5S + 3(301 - 2S) = 813
5S + 903 - 6S = 813
- S = -90
S = 90
Substitute the value of S into equation (5):
2(90) + L = 301
180 + L = 301
L = 121
Therefore, each small ice sculpture costs $90 and each large ice sculpture costs $121.