SOLUTION: An artist makes three types of ceramic statues (large, medium, and small) at a monthly cost of $1390 for 250 statues. The manufacturing costs for the three types are $7, $6, and $5

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Question 1151909: An artist makes three types of ceramic statues (large, medium, and small) at a monthly cost of $1390 for 250 statues. The manufacturing costs for the three types are $7, $6, and $5. If the statues sell for $26, $18, and $15, respectively, how many of each type should be made to produce $4,370 in monthly revenue?
thank you so whoever solves this. I hope its MATHLOVER1. (• ◡•) ok bai

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

its MATHLOVER1. (• ◡•) ok
large: L -> the manufacturing costs $7
medium: M-> the manufacturing costs $6
small: S-> the manufacturing costs $5
cost: $1390 for 250 statues:
L%2BM%2BS=250........eq.1
7L%2B6M%2B5S=1390 ........eq.2
for revenue
26L%2B18M%2B15S=4370 ........eq.3
-----------------------------------------------------solve the system
L=250-M-S........eq.1a
L=1390%2F7-6M%2F7-5S%2F7 ........eq.2
----------------------------------------------- =>
250-M-S=1390%2F7-6M%2F7-5S%2F7
6M%2F7-M-S%2B5S%2F7=1390%2F7-250......both sides multiply by 7
6M-7M-7S%2B5S=1390-1750
-M-2S=-360.....solve for M
M=360-2S...............eq.1b
go to
26L%2B18M%2B15S=4370 ........eq.3.............substitute L from eq.1 and M from eq.1b
26%28250-%28360-2S%29-S%29%2B18%28360-2S%29%2B15S=4370 ............solve for S
26%28250-360%2B2S-S%29%2B18%28360-2S%29%2B15S=4370
6500-9360%2B52S-26S%2B6480-36S%2B15S=4370
3620%2B5S=4370
5S=4370-3620
5S=750
S=750%2F5
highlight%28S=150%29
go to M=360-2S...............eq.1a, substitute S
M=360-2%2A150
M=360-300
highlight%28M=60%29
go to L=250-M-S........eq.1a , substitute S and M
L=250-60-150
L=250-210
highlight%28L=40%29
answer: highlight%28L=40%29, highlight%28M=60%29, and highlight%28S=150%29 should be made to produce $4370 in monthly revenue

check: If the number of statues above sell for $26, $18, and $15, respectively will produce $4370 in monthly revenue
4370=26L%2B18M%2B15S
4370=26%2A40%2B18%2A60%2B15%2A150
4370=1040%2B1080%2B2250
4370=4370 which confirms our answer