SOLUTION: Working her way through school, Kathy works two part-time jobs for a total of 23 hours a week. Job A pays $5.80 per hour, and Job B pays $7.30 per hour. How many hours did she work

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Question 1157183: Working her way through school, Kathy works two part-time jobs for a total of 23 hours a week. Job A pays $5.80 per hour, and Job B pays $7.30 per hour. How many hours did she work at each job the week that she made $148.40? (Round to two decimal places if necessary.)
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = number of hours shw worked for job A.
y = number of hours she worked for job B.
x + y = 23
5.8x + 7.3y = 148.4
these are two equations that need to be solved simultaneously.
the first tells her the total hours she worked.
the second tells her the total amount of money she made.
multiply both sides of the first equation by 5.8 and leave the second equation as is to get:
5.8x + 5.8y = 133.4
5.8x + 7.3y = 148.4
subtract the first equation from the second to get:
0x + 1.5y = 15 which becomes:
1.5y = 15
solve for y to get:
y = 10
this makes x = 13 because 13 + 10 = 23
replace x with 13 and y with 10 in the second equation to get:
5.8 * 13 + 7.3 * 10 = 148.4
evaluate to get:
148.4 = 148.4
this confirms the values of x = 13 and y = 10 are good.
your solution is:
she worked 13 hours for job A and 10 hours for job B.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Working her way through school, Kathy works two part-time jobs for a total of 23 hours a week. Job A pays $5.80 per hour, and Job B pays $7.30 per hour. How many hours did she work at each job the week that she made $148.40? (Round to two decimal places if necessary.)
Let number of hours she worked for the $5.80 per-hour job be F

Then the number of hours she worked for the $7.30 per-hour job = 23 - F

We then get: 5.8F + 7.3(23 - F) = 148.4

5.8F + 167.9 - 7.3F = 148.4

5.8F - 7.3F = 148.4 - 167.9

 - 1.5F = - 19.5

Number of hours she worked for the $5.80 per-hour job, or 

Do you think you can now find the number of hours for the other job? 

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