SOLUTION: Melinda is a single mom, working two jobs just to make ends meet. She makes $11.00 an hour as a receptionist in dental office and on weekends she works at a shoe store making $8.00

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Melinda is a single mom, working two jobs just to make ends meet. She makes $11.00 an hour as a receptionist in dental office and on weekends she works at a shoe store making $8.00      Log On


   

Question 1077203: Melinda is a single mom, working two jobs just to make ends meet. She makes $11.00 an hour as a receptionist in dental office and on weekends she works at a shoe store making $8.00 an hour. One week she worked 49 hours and made $506. How many hours did she work at each job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs she worked at dentsl office
+49+-+t+ = time in hrs she worked at shoe store
Let +p+ = her pay for working that week at dental office
+506+-+p+ = her pay for working that week at shoe store
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Equation for the dental office:
(1) +p+=+11t+
Equation for the shoe store:
(2) +506+-+p+=+8%2A%28+49+-+t+%29+
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Substitute (1) into (2)
(2) +506+-+11t+=+8%2A%28+49+-+t+%29+
(2) +506+-+11t+=+392+-+8t+
(2) +3t+=+114+
(2) +t+=+38+
and
+49+-+t+=+49+-+38+
+49+-+t+=+11+
She worked 38 hrs at the dental office
and 11 hrs at the shoe store
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check:
(1) +p+=+11t+
(1) +p+=+11%2A38+
(1) +p+=+418+
and
(2) +506+-+p+=+8%2A%28+49+-+t+%29+
(2) +506+-+p+=+8%2A11+
(2) +p+=+506+-+88+
(2) +p+=+418+
OK