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An electrician charges a service charge of $40, plus $25 per hour. If the final bill for an electrical repair is $170, which equation represents the cost for \( h \), the number of hours?

A. \( 25(h + 40) = 170 \)

B. \( 40(h + 25) = 170 \)

C. \( 40 + 25h = 170 \)

D. \( 25 + 40h = 170 \)

Answer :

Final answer:

Option 1: 25(h + 40) = 170 represents the cost for h, the number of hours.

Explanation:

Let "h" be the number of hours of work done by the electrician. From the given information, we know that the electrician charges a service charge of $40, plus $25 per hour of work. This can be represented mathematically as:

Cost = 25h + 40

If the final bill for an electrical repair is $170, we can set up an equation to solve for "h". Substituting the given values, we get:

170 = 25h + 40

Solving for "h", we get:

25h = 130

h = 5.2

Therefore, the number of hours of work done by the electrician is 5.2 hours.

Now, we need to find which of the given options represents the original equation for the cost of work done by the electrician. We can plug in the value of "h" we found to see which equation holds true.

Option 1: 25(h + 40) = 25(5.2 + 40) = 1070 which is not equal to the actual final cost of $170.

Option 2: 40(h + 25) = 40(5.2 + 25) = 1180 which is not equal to the actual final cost of $170.

Option 3: 40 + 25h = 40 + 25(5.2) = 180 which is not equal to the actual final cost of $170.

Option 4: 25 + 40h = 25 + 40(5.2) = 205 which is not equal to the actual final cost of $170.

Therefore, the option that represents the correct equation is:

Option 1: 25(h + 40) = 170

This equation simplifies to:

25h + 1000 = 170

25h = 70

h = 2.8

Therefore, the number of hours of work done by the electrician is 2.8 hours, and the equation 25(h + 40) = 170 represents the cost for "h", the number of hours.

Being able to set up and solve equations is an important skill in mathematics and is useful in many real-life situations, such as in calculating costs for services.

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