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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Tucker gets paid at home for doing extra chores. Last week, he did $6$ loads of laundry and $8$ loads of dishes, and his parents paid him $\$22$ . The week before, he finished $6$ loads of laundry and $4$ loads of dishes, earning a total of $\$14$ . How much does Tucker earn for completing each type of chore? $\newline$ Tucker earns $\$\_\_\_\_$ per load of laundry and $\$\_\_\_\_$ per load of dishes.

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Solve a system of equations using elimination: word problems

Full solution

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

\newline

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

6

loads of laundry and

8

loads of dishes, and his parents paid him

\$22

. The week before, he finished

6

loads of laundry and

4

loads of dishes, earning a total of

\$14

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

\newline

Tucker earns

\$\_\_\_\_

per load of laundry and

\$\_\_\_\_

per load of dishes.

Define variables: Define the variables for the amount Tucker earns per load of laundry and per load of dishes. $\newline$ Let $x$ be the amount Tucker earns per load of laundry. $\newline$ Let $y$ be the amount Tucker earns per load of dishes.
Write equations: Write the system of equations based on the given information. $\newline$ From the first week: $6$ loads of laundry and $8$ loads of dishes for $\$22$ . $\newline$ $6x + 8y = 22$ $\newline$ From the week before: $6$ loads of laundry and $4$ loads of dishes for $\$14$ . $\newline$ $6x + 4y = 14$
Use elimination: Use elimination to solve the system of equations. $\newline$ We can eliminate $x$ by subtracting the second equation from the first equation. $\newline$ $(6x + 8y) - (6x + 4y) = 22 - 14$
Perform subtraction: Perform the subtraction to find the value of $y$ . $\newline$ $6x + 8y - 6x - 4y = 22 - 14$ $\newline$ $8y - 4y = 8$ $\newline$ $4y = 8$ $\newline$ $y = \frac{8}{4}$ $\newline$ $y = 2$
Substitute value: Substitute the value of $y$ into one of the original equations to solve for $x$ . Using the second equation: $6x + 4(2) = 14$ $6x + 8 = 14$ $6x = 14 - 8$ $6x = 6$ $x = 6 / 6$ $x = 1$
Check solution: Check the solution by substituting both values into the other original equation. $\newline$ Using the first equation: $6(1) + 8(2) = 22$ $\newline$ $6 + 16 = 22$ $\newline$ $22 = 22$ $\newline$ The solution checks out.

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