SOLUTION: how many tons of hay at $125 per ton and $75 per ton must be purchased to have 100 tons of hay worth $9000?

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Question 221223: how many tons of hay at $125 per ton and $75 per ton must be purchased to have 100 tons of hay worth $9000?
Found 2 solutions by sofiyac, josmiceli:
Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
125x%2B75y=9000
x%2By=100 so we have to solve this system of equations
x=100-y
125%28100-y%29%2B75y=9000
12500-125y%2B75y=9000
12500-50y=9000
-50y=9000-12500
-50y=-3500 divide both sides by -50
y=70
x=100-70=30
so we need 30 tons at $125/ton and 70 tons at $75/ton




Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = tons of $125/ton hay used
Let b = tons of $75/ton hay used
given:
(1) a+%2B+b+=+100
(2) 125a+%2B+75b+=+9000
---------------------------
Multiply both sides of (1) by 75 and
subtract from (2)
(2) 125a+%2B+75b+=+9000
(1) -75a+%2B+-75b+=+-7500
50a+=+1500
a+=+30
and, since
a+%2B+b+=+100
30+%2B+b+=+100
b+=+70
30 tons of $125/ton hay and 70 tons of $75/ton hay
must be purchased
check:
(2) 125a+%2B+75b+=+9000
125%2A30+%2B+75%2A70+=+9000
3750+%2B+5250+=+9000
9000+=+9000
OK