SOLUTION: A student works two part-time jobs. He earns $8 an hour for working at a college library and $15 an hour for construction work. To save time for study, he limits his work to 25 hou

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A student works two part-time jobs. He earns $8 an hour for working at a college library and $15 an hour for construction work. To save time for study, he limits his work to 25 hou      Log On


   

Question 791999: A student works two part-time jobs. He earns $8 an hour for working at a college library and $15 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 $300 a week?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = number of hours worked at library
+25+-+t+ = number of hours worked at construction
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+8t+%2B+15%2A%28+25+-+t+%29+=+300+
+8t+%2B+375+-+15t+=+300+
+7t+=+375+-+300+
+7t+=+75+
+t+=+10.714+
Neglecting fractions of hours, he can work 10 hrs
at library and still earn $300/wk
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check:
+8t+%2B+15%2A%28+25+-+t+%29+%3E=+300+
+8%2A10+%2B+15%2A%28+25+-+10+%29+%3E=+300+
+80+%2B+15%2A15+%3E=+300+
+80+%2B+225+%3E=+300+
+325+%3E=+300+
OK
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Suppose he works 11 hrs at library
+8t+%2B+15%2A%28+25+-+t+%29+%3E=+300+
+8%2A11+%2B+15%2A%28+25+-+11+%29+%3E=+300+
+88+%2B+15%2A14+%3E=+300+
+88+%2B+210+%3E=+300+
+298+%3E=+300+
This is not true, so he must limit hrs worked
at library to 10 hrs