Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Eli gets paid at home for doing extra chores. Last week, he did $8$ loads of laundry and $3$ loads of dishes, and his parents paid him $\$35$ . The week before, he finished $8$ loads of laundry and $6$ loads of dishes, earning a total of $\$38$ . How much does Eli earn for completing each type of chore? $\newline$ Eli earns $\$$ _ per load of laundry and $\$$ _ per load of dishes.

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Eli gets paid at home for doing extra chores. Last week, he did

8

loads of laundry and

3

loads of dishes, and his parents paid him

\$35

. The week before, he finished

8

loads of laundry and

6

loads of dishes, earning a total of

\$38

. How much does Eli earn for completing each type of chore?

\newline

Eli earns

\$

_____ per load of laundry and

\$

_____ per load of dishes.

Define Variables: Let's denote the price per load of laundry as $l$ and the price per load of dishes as $d$ . Eli's earnings for $8$ loads of laundry and $3$ loads of dishes are $\$35$ , leading to the equation $8l + 3d = 35$ .
Set Up Equations: From the previous week, Eli did $8$ loads of laundry and $6$ loads of dishes for $\$38$ , giving us the equation $8l + 6d = 38$ .
Eliminate Variable: To eliminate one variable, we'll focus on eliminating $l$ . Multiply the first equation by $-1$ to align the coefficients of $l$ for subtraction. $-8l - 3d = -35$ .
Solve for $d$ : Add this equation to the second equation: $-8l - 3d + 8l + 6d = -35 + 38$ , simplifying to $3d = 3$ .
Substitute and Simplify: Solve for $d$ : $d = \frac{3}{3}$ , which simplifies to $d = 1$ .
Solve for $l$ : Substitute $d = 1$ back into the first equation: $8l + 3(1) = 35$ . Simplify to $8l + 3 = 35$ .
Solve for $l$ : Substitute $d = 1$ back into the first equation: $8l + 3(1) = 35$ . Simplify to $8l + 3 = 35$ . Solve for $l$ : $8l = 35 - 3$ , which simplifies to $8l = 32$ . Then, $l = \frac{32}{8}$ , which simplifies to $l = 4$ .