Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ The Ferguson family is looking to rent a large truck for their upcoming move. With Rob's Moving, they would pay $\$8$ for the first day plus $\$9$ per additional day. With Clarksville Rent-a-Truck, in comparison, the family would pay $\$16$ for the first day plus $\$1$ per additional day. Before deciding on which company to use, Mrs. Ferguson wants to find out what number of additional days would make the two choices equivalent with regards to cost. How many additional days would that be? What would the total cost be? $\newline$ If the Ferguson family rented the truck for _ additional days, they would pay $\$$ _ either way.

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using substitution: word problems

Full solution

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

\newline

The Ferguson family is looking to rent a large truck for their upcoming move. With Rob's Moving, they would pay

\$8

for the first day plus

\$9

per additional day. With Clarksville Rent-a-Truck, in comparison, the family would pay

\$16

for the first day plus

\$1

per additional day. Before deciding on which company to use, Mrs. Ferguson wants to find out what number of additional days would make the two choices equivalent with regards to cost. How many additional days would that be? What would the total cost be?

\newline

If the Ferguson family rented the truck for ___ additional days, they would pay

\$

___ either way.

Define Variables: Let's define the variables: $\newline$ Let $x$ be the number of additional days. $\newline$ Let $R$ be the total cost of renting from Rob's Moving. $\newline$ Let $C$ be the total cost of renting from Clarksville Rent-a-Truck.
Equation for Rob's Moving: Write the equation for Rob's Moving: $\newline$ $R = 8 + 9x$ (since the first day is $\$8$ and each additional day is $\$9$ ).
Equation for Clarksville Rent-a-Truck: Write the equation for Clarksville Rent-a-Truck: $C = 16 + 1x$ (since the first day is $\$16$ and each additional day is $\$1$ ).
Set Equations Equal: Set the two equations equal to each other to find the number of days where the cost is the same: $8 + 9x = 16 + 1x$
Subtract $x$ Terms: Subtract $1x$ from both sides to get the $x$ terms on one side: $\newline$ $8 + 9x - 1x = 16 + 1x - 1x$ $\newline$ $8 + 8x = 16$
Subtract $8$ : Subtract $8$ from both sides to solve for $x$ : $\newline$ $8 + 8x - 8 = 16 - 8$ $\newline$ $8x = 8$
Divide by $8$ : Divide both sides by $8$ to find the value of x: $\newline$ $\frac{8x}{8} = \frac{8}{8}$ $\newline$ $x = 1$
Find Total Cost: Now that we know $x = 1$ , we can find the total cost for that number of additional days. We can use either $R$ or $C$ since we are looking for the point where they are equal. $\newline$ Let's use $R$ : $\newline$ $R = 8 + 9(1)$ $\newline$ $R = 8 + 9$ $\newline$ $R = 17$