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A plumber charges [tex]$\$[/tex]130[tex]$ to start a job plus $[/tex]\[tex]$56$[/tex] per hour. How many hours did she work if the total bill is [tex]$\$[/tex]214$?

This problem can be modeled with this equation:

[tex]\[ 130 + 56x = 214 \][/tex]

Step 1: Apply the subtraction property of equality.
Which value do you need to subtract?
[tex]\[ 130 \][/tex]

Step 2: Apply the division property of equality.
Which operation should be performed to make the coefficient of [tex]\( x \)[/tex] equal to 1?

Step 3: Which statement expresses the answer in the context of the problem?

Sagot :

GinnyAnswer
Sure, let's go through the steps to solve the problem step-by-step.

1. Identify the given values and establish the equation:
- The plumber charges a start fee of [tex]$130. - The plumber charges $[/tex]56 per hour.
- The total bill is [tex]$214. Let \(x\) represent the number of hours the plumber worked. The equation for the total bill can be written as: \[ 130 + 56x = 214 \] 2. Isolate the variable term by applying the subtraction property of equality: - Subtract the start fee of $[/tex]130 from the total bill to find out how much of the bill is attributed to the hourly work.
[tex]\[ 214 - 130 \][/tex]

Performing the subtraction, we get:
[tex]\[ 84 \][/tex]

So the modified equation becomes:
[tex]\[ 56x = 84 \][/tex]

3. Solve for [tex]\(x\)[/tex] by applying the division property of equality:
- To make the coefficient of [tex]\(x\)[/tex] equal to 1, divide both sides of the equation by 56.
[tex]\[ x = \frac{84}{56} \][/tex]

Performing the division, we find:
[tex]\[ x = 1.5 \][/tex]

4. Interpret the result in the context of the problem:
- The plumber worked for 1.5 hours.

Therefore, your detailed step-by-step solution shows that the plumber worked for [tex]\(1.5\)[/tex] hours if the total bill is $214.
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