SOLUTION: You worked 14 hours last week and earned a total of $96.00 before taxes. Your job as a lifeguard pays $8.00 per hour, and your job as a cashier pays $6.00 per hour. How many hour

Question 106210This question is from textbook McDougal Littell Algebra 2
: You worked 14 hours last week and earned a total of $96.00 before taxes. Your job as a lifeguard pays $8.00 per hour, and your job as a cashier pays $6.00 per hour. How many hours did you work at each job?

I have a problem similar to the above. But can't remember how to set up the solution. My guess is 8x + 6y = 96 This question is from textbook McDougal Littell Algebra 2

Found 2 solutions by bucky, jamaicanboy:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You have a good start on this problem. You have said that x represents the number of hours
that the person worked as a lifeguard. And you have also said that y represents the number
of hours the person worked as an cashier. That being the case, your equation:
.
8x + 6y = 96
.
is correct ... $8 times the number of hours worked as a lifeguard plus $6 times the number
of hours worked as an cashier must equal $96.
.
Next you need to recognize that the total number of hours ... x + y ... is equal to 14 hours.
Therefore you can say that the number of lifeguard hours x must be the total 14 hours less
the cashier hours. That means x = 14 - y. So for x in the $ equation you can substitute
14 - y and the equation becomes:
.
8(14 - y) + 6y = 96
.
Multiply out the left side by multiplying 8 times both terms in the parentheses to get:
.
112 - 8y + 6y = 96
.
combine the -8y and the +6y to get -2y and the equation becomes:
.
112 - 2y = 96
.
Get rid of the 112 on the left side by subtracting 112 from both sides. When you do that
subtraction the equation becomes:
.
-2y = -16
.
Solve for y by dividing both sides of this equation by -2 to get:
.
y = -16/-2 = 8
.
This means the person worked 8 hours as an cashier. Since the total number of hours worked
is 14, that means that the remaining 6 hours were worked as a lifeguard.
.
Let's check. If the person works 6 hours as a lifeguard at $8 per hour, he or she earns $48.
Then the person works 8 hours as a cashier at $6 per hour, earning another $48. The total
earnings are $48 + $48 for a total of $96. This checks, so the answers are correct ...
6 hours as a lifeguard and 8 hours as a cashier.
.
Hope this helps you to understand the problem.
.
Answer by jamaicanboy(1) (Show Source): You can put this solution on YOUR website!
8x + 6y = 96
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