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

This problem can be modeled with this equation:

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

Step 1: Which operation should be performed to isolate the variable term?
- Apply the subtraction property of equality.
- Which value do you need to subtract?
[tex]\[ 130 \][/tex]

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


Sagot :

To determine the number of hours the plumber worked, given the total bill of \[tex]$214, the starting fee of \$[/tex]130, and the hourly rate of \[tex]$56, we can break down the problem step-by-step as follows: ### Step 1: Isolate the variable term The given equation is: \[ 130 + 56x = 214 \] To isolate the term containing \( x \) (the number of hours worked), we need to get rid of the starting fee of \$[/tex]130 on the left side of the equation by subtracting \$130 from both sides of the equation:

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

This simplifies to:

[tex]\[ 56x = 84 \][/tex]

### Step 2: Solve for [tex]\( x \)[/tex]

Now, we need to solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. Since [tex]\( 56x \)[/tex] means [tex]\( 56 \)[/tex] times [tex]\( x \)[/tex], we can isolate [tex]\( x \)[/tex] by dividing both sides of the equation by 56 to make the coefficient of [tex]\( x \)[/tex] equal to 1:

[tex]\[ \frac{56x}{56} = \frac{84}{56} \][/tex]

This simplifies to:

[tex]\[ x = 1.5 \][/tex]

### Conclusion

Thus, the number of hours the plumber worked is 1.5 hours.
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