Question

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A consulting engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour. A customer received a bill for $425 fir a certain job. If the assistant worked 5 hours less than the engineer, how much time did each bill on the job?

Engineer: _____ hr
Assistant: ______ hr

Answer 1

Engineer: 9.5 hr

Assistant: 4.5 hr

Explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

• Let x be the number of hours the engineer worked.
• Let y be the number of hours the assistant worked.

Given the engineer's time is billed at $40 per hour, and her assistant's is billed at $10 per hour, and a customer received a bill for $425 for a certain job:

• 
  `40x+10y=425`

Given the assistant worked 5 hours less than the engineer:

• 
  `y=x-5`

Therefore, the system of equations that represents the problem is:

`\begin{cases}40x+10y=425\\ \quad \qquad \;\;\;y=x-5\end{cases}`

Substitute the second equation into the first equation to eliminate y:

`40x+10(x-5)=425`

Solve the equation for x to find the number of hours the engineer worked:

`\begin{aligned}40x+10(x-5)&=425\\40x+10x-50&=425\\50x-50&=425\\50x&=475\\x&=9.5\end{aligned}`

Therefore, the engineer worked 9.5 hours.

Substitute the found value of x into the second equation and solve for y to find the number of hours the assistant worked:

`\begin{aligned}y&=x-5\\y&=9.5-5\\y&=4.5\end{aligned}`

Therefore, the assistant worked 4.5 hours.