Question

Tuto Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The freshman and sophomore classes at Danville High School are decorating floats for homecoming. The freshmen have already spent $44 on their float, plus they need to buy floral sheeting that costs $101 per roll. The sophomores, who have spent $55 so far on theirs, still need to purchase vinyl grass at $100 per roll. Both classes plan to buy the same number of rolls, since they have the same area to cover. By coincidence, the two floats will have the same total cost in the end. How much will each class spend in total? How many rolls will each tlass be buying? The two classes will have each spend $ in total by buying rolls.

Answer 1

Let x be the number of rolls purchased and y the total cost.

The equation that describes the total cost for freshmen is:

$44+101x=y$

The equation that describes the total cost for sophomores is:

$55+100x=y$

Make both equations for y equal and solve for x:

$\begin{gathered} 44+101x=55+100x \\ 101x-100x=55-44 \\ x=11 \end{gathered}$

Use the value of x to find y:

$\begin{gathered} 55+100(11)=y \\ 55+1100=y \\ 1155=y \end{gathered}$

It means that the two classes will have each spend $1155 in total by buying 11 rolls.