SOLUTION: The cost varied linearly with the number of hours the staff worked. When the staff worked 200 hours the cost was $1725, and when the staff worked 100 hours the cost was $925. What

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The cost varied linearly with the number of hours the staff worked. When the staff worked 200 hours the cost was $1725, and when the staff worked 100 hours the cost was $925. What       Log On


   

Question 1084608: The cost varied linearly with the number of hours the staff worked. When the staff worked 200 hours the cost was $1725, and when the staff worked 100 hours the cost was $925. What would it cost if the staff worked 150 hours?

Got stumped on this question, any help in solving it would be appreciated! Thanks.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
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The cost varied linearly with the number of hours the staff worked.
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y=mx%2Bb
x, hours
y, cost

Two points from description as (x,y):
(200, 1725) and (100, 925).

m=%281725-925%29%2F%28200-100%29
m=800%2F100

m=8
-
b=y-mx
b=925-8%2A100
b=125
highlight%28y=8x%2B125%29

-
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What would it cost if the staff worked 150 hours?
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You actually do not need the equation. Simple linear interpolation should be enough. 150 is exactly in the middle of 100 and 200 hours. Find therefore the exact middle of $1725 and $925:
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$1325