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Paul's usual hourly wage is $x$𝑥. He works for 66 hours at this wage and then 22 more hours at an increased wage of $(2x+3)$(2𝑥+3). If he earns $146$146 for the 88 hours, write an equation and solve it to find Paul's usualy hourly wage.

Question

Paul's usual hourly wage is xx𝑥. He works for 66 hours at this wage and then 22 more hours at an increased wage of (2x+3)(2x+3)(2𝑥+3). If he earns 146146146 for the 88 hours, write an equation and solve it to find Paul's usualy hourly wage.

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Solution

The problem can be solved by setting up an equation based on the information given.

First, we know that Paul's usual hourly wage is xx and he works for 66 hours at this wage. So, his earnings for these 66 hours would be 66x66x.

Next, we know that he works for 22 more hours at an increased wage of (2x+3)(2x+3). So, his earnings for these 22 hours would be 22(2x+3)22(2x+3).

Finally, we know that his total earnings for the 88 hours is $146. So, we can set up the following equation to represent this situation:

66x+22(2x+3)=14666x + 22(2x+3) = 146

Solving this equation will give us the value of xx, which is Paul's usual hourly wage.

Let's simplify the equation:

66x+44x+66=14666x + 44x + 66 = 146

Combine like terms:

110x+66=146110x + 66 = 146

Subtract 66 from both sides:

110x=80110x = 80

Finally, divide both sides by 110 to solve for xx:

x=80/110=0.727x = 80/110 = 0.727

So, Paul's usual hourly wage is approximately $0.73.

This problem has been solved

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