bob worked 32 hours per week at his job. his boss offers him a full-time position (40 hours per wee) and a $2 per hour raise. He now will be making $200 more per week. what was his hourly rate before the raise?
old rate --- $x
new rate --- $ x+2
wage per week at old rate = $ 32x
wage per week at new rate with more hours = 40(x+2)
40(x+2) - 32x = 200
easy to solve
To find Bob's hourly rate before the raise, we can start by calculating his total weekly income before the raise. Let's assume his hourly rate before the raise is x.
Before the raise, Bob worked 32 hours per week, so his weekly income was 32x dollars.
After accepting the full-time position, Bob works 40 hours per week. Since his boss offers him a $2 per hour raise, his new hourly rate will be (x + 2) dollars.
With the full-time position and the raise, Bob's new weekly income is 40(x + 2) dollars.
According to the problem, Bob's new weekly income is $200 more than before. So, we can set up the equation:
40(x + 2) = 32x + 200
Now, let's solve the equation to find the value of x, Bob's hourly rate before the raise.
40x + 80 = 32x + 200 (distributing the 40)
40x - 32x = 200 - 80 (subtracted 32x from both sides)
8x = 120 (simplified)
x = 120 / 8 (divided both sides by 8)
x = 15
Therefore, Bob's hourly rate before the raise was $15.