Question

equationsWrite a system of equations to describe the situation below, solve using elimination, and fill inche blanks.lada gets paid at home for doing extra chores. Last week, she did 1 load of laundry and 8oads of dishes, and her parents paid her $26. The week before, she finished 3 loads ofaundry and 8 loads of dishes, earning a total of $30. How much does Jada earn forcompleting each type of chore?

Answer 1

In this problem, we are going to write and solve a system of equations based on a real world situation.

Last week, she did 1 load of laundry and 8 loads of dishes, and her parents paid her $26. The week before, she finished 3 loads of laundry and 8 loads of dishes, earning a total of $30.

To begin, we need to create variables for the unknown cost of each chore.

Let x represent laundry, and let y represent dishes.

From the first equation, we can write the equation:

`x+8y=26`

We can write the second equation as:

`3x+8y=30`

Together, we have the system:

`\begin{cases}x+8y={26} \\ 3x+8y={30}\end{cases}`

Multiply the first equation by -1, then add it to the second equation:

`\begin{gathered} \begin{cases}-1(x+8y={26)} \\ 3x+8y={30}\end{cases} \\ \\ \begin{cases}-x-8y={-26} \\ 3x+8y={30}\end{cases} \\ \\ (-x+3x)+(-8y+8y)=-26+30 \\ 2x=4 \end{gathered}`

We can divide the remaining equation by 2 on both sides:

`\begin{gathered} (2x)/(2)=(4)/(2) \\ \\ x=2 \end{gathered}`

Lada made $2 per load of laundry.

We can use the value of x in the first equation to find the value of y. Substitute x = 2:

`2+8y=26`

Subtract 2 from both sides:

`8y=24`

Divide by 8 on both sides:

`y=3`

Lada made $3 per load of dishes.