Question

Faith is working two summer jobs, making $13 per hour lifeguarding and $12 perhour washing cars. Last week Faith worked a total of 10 hours and earned a totalof $124. Using the variables and equations from the previous problem, use eitherelimination or substitution to determine the number of hours Faith workedlifeguarding last week and the number of hours she worked washing cars lastweek.

Answer 1

VARIABLES:

Let the variable "L" represent the number of hours Faith spends lifeguarding and "W" be the number of hours spent washing cars.

EQUATIONS:

Lifeguarding pays $13 per hour while washing cars pay $12 per hour.

The total amount Faith earned is $124. Therefore, we can have as an equation:

`13L+12W=124`

The total number of hours Faith worked is 10 hours. We can therefore write an equation to represent this to be:

`L+W=10`

SOLUTION:

The system of equations can be written to be:

`\begin{gathered} 13L+12W=124\text{ -----------(1)} \\ L+W=10\text{ -----------(2)} \end{gathered}`

To use the Elimination method, we can multiply Equation (2) by 12 to make the coefficients of W in the 2 equations be equal:

`\begin{gathered} (2)*12 \\ \Rightarrow12L+12W=120\text{ -----------(3)} \end{gathered}`

Subtract equation (3) from (1) to eliminate W:

`\begin{gathered} 13L-12L+12W-12W=124-120 \\ L=4 \end{gathered}`

We can find the value of W by substituting for L into equation (2):

`\begin{gathered} 4+W=10 \\ W=10-4 \\ W=6 \end{gathered}`

ANSWERS:

`\begin{gathered} L=4 \\ W=6 \end{gathered}`