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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineThe Ferguson family is looking to rent a large truck for their upcoming move. With Rob's Moving, they would pay $8\$8 for the first day plus $9\$9 per additional day. With Clarksville Rent-a-Truck, in comparison, the family would pay $16\$16 for the first day plus $1\$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?\newlineIf the Ferguson family rented the truck for ___ additional days, they would pay $\$___ either way.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineThe Ferguson family is looking to rent a large truck for their upcoming move. With Rob's Moving, they would pay $8\$8 for the first day plus $9\$9 per additional day. With Clarksville Rent-a-Truck, in comparison, the family would pay $16\$16 for the first day plus $1\$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?\newlineIf the Ferguson family rented the truck for ___ additional days, they would pay $\$___ either way.
  1. Define Variables: Let's define the variables:\newlineLet xx be the number of additional days.\newlineLet RR be the total cost of renting from Rob's Moving.\newlineLet CC be the total cost of renting from Clarksville Rent-a-Truck.
  2. Equation for Rob's Moving: Write the equation for Rob's Moving:\newlineR=8+9xR = 8 + 9x (since the first day is $8\$8 and each additional day is $9\$9).
  3. Equation for Clarksville Rent-a-Truck: Write the equation for Clarksville Rent-a-Truck: C=16+1xC = 16 + 1x (since the first day is $16\$16 and each additional day is $1\$1).
  4. 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+1x8 + 9x = 16 + 1x
  5. Subtract xx Terms: Subtract 1x1x from both sides to get the xx terms on one side:\newline8+9x−1x=16+1x−1x8 + 9x - 1x = 16 + 1x - 1x\newline8+8x=168 + 8x = 16
  6. Subtract 88: Subtract 88 from both sides to solve for xx: \newline8+8x−8=16−88 + 8x - 8 = 16 - 8\newline8x=88x = 8
  7. Divide by 88: Divide both sides by 88 to find the value of x:\newline8x8=88\frac{8x}{8} = \frac{8}{8}\newlinex=1x = 1
  8. Find Total Cost: Now that we know x=1x = 1, we can find the total cost for that number of additional days. We can use either RR or CC since we are looking for the point where they are equal.\newlineLet's use RR:\newlineR=8+9(1)R = 8 + 9(1)\newlineR=8+9R = 8 + 9\newlineR=17R = 17

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