SOLUTION: A student works two part-time jobs. He earns $9 an hour for working at the college library and $14 an hour for construction work. To save time for study, he limits his work to 25 h

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Question 1016308: A student works two part-time jobs. He earns $9 an hour for working at the college library and $14 an hour for construction work. To save time for study, he limits his work to 25 hours a week. If he enjoys the work at the library more, how many hours can he work at the library and still earn at least $285 a week?
Found 2 solutions by addingup, josgarithmetic:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
L+C= 25, so construction alone: C = 25-L We will use this value for C next
9L+14C =>285 Now substitute for C:
9L+14(25-L) => 285
9L+350-14L=> 285 Subtract 350, both sides, and add L on left:
-5L => -65 Divide both sides by 5 and remember:1) -/- = + and 2) the < or > sign is reversed when we divide - and - and thus have a resulting +:
L =< 13 He needs to work no more than 13 hours at the library to make at least 285.
J

Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
x   construction work hours
y   library work hours


Account for wages
9y+14x>=285

Account for work time
x+y<=25

System of inequalities, system%2814x%2B9y%3E=285%2Cx%2By%3C=25%29

A possible method can be to graph the system system%28y%3E=-%2814%2F9%29x%2B95%2F3%2Cy%3C=-x%2B25%2Cx%3E=0%2Cy%3E=0%29

Here is a graph without filling any of the inequality regions:
graph%28400%2C400%2C-2%2C30%2C-2%2C30%2C-%2814%2F9%29x%2B95%2F3%2C-x%2B25%29

The most hours at the library is want is wanted, and in examining the graph, this will be at the intersection point of the two lines. That could be THE BEST answer.
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You can do the algebra if you want, equating the two expressions for y, solve for x and y; and find x=12 for construction job hours, and y=13 for library work hours.