SOLUTION: Rita grossed $435 one week working 52 hours. Rita's employer pays time-and-a-half for all hours over 40 hours. With this information, can you determine Rita's regular salary wage?

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Question 1208696: Rita grossed $435 one week working 52 hours. Rita's employer pays time-and-a-half for all hours over 40 hours. With this information, can you determine Rita's regular salary wage?
Textbook Solution
1. We are looking for hourly wage.
2. Let x = regular hourly wage for Rita's
3. Set up a table
Table
Regular Hours = 40
Hourly wage = x
Salary = 40x
Overtime hours = 12
Hourly wage = 1.5x
Salary = 12(1.5x) = 18x
The correct equation is 40x + 12(1.5)x = 435
My equation is 40x + 12(1.5) = 435
Question
Why must 12 hours be multiplied by 1.5x instead of simply 1.5? Understand? You say?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) (Show Source):
You can put this solution on YOUR website!
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The correct equation is 40x + 12(1.5)x = 435
My equation is 40x + 12(1.5) = 435
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The time-and-a-half pay rate is 1.5x.
regular time pay + time-and-a-half pay =435
so

Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

In any equation where terms are being combined using addition or subtraction, the terms must represent the same kinds of things. Your equation is

40x + 12(1.5) = 435

In that equation, "40x" is her pay for 40 hours at rate x, and 435 is her total pay. So those two terms both represent amounts of pay.

But the term 12(1.5) does not represent an amount of pay. "12 hours" times "1.5" simply gives 18 hours.

As you show earlier in your post, "12(1.5x)" is her pay for the overtime hours. So the correct equation, showing "pay for normal hours, plus pay for overtime, equals total pay" is

40(x) + 12(1.5x) = 435