Question

Solve the real-world situation by using the substitution method. A movie theater sells popcorn and fountain drinks. Brett buys 1 popcorn bucket and 3fountain drinks for his family, which costs him a total of $30.50. Sarah buys 3 popcornbuckets and 4 fountain drinks for her family, which costs her a total of $47.75. If prepresents the number of popcorn buckets and d represents the number of drinks, then the(30.50 = p + 3d47.75 = 3p + 4dsystem of equationscan be used to represent this situation.Find the cost of a popcorn bucket and the cost of a fountain drink.The cost of a bucket of popcorn is $|and the cost of a fountain soda is $

Answer 1

Given:

$\begin{gathered} p+3d=30.50\ldots\text{ (1)} \\ 3p+4d=47.75\ldots\text{ (2)} \end{gathered}$

Multiply equation (1) by 3 and subtract from equation(2)

$\begin{gathered} 3p+4d-3p-9d=47.75-91.50 \\ -5d=-43.75 \\ d=8.75 \end{gathered}$

Substitute d=8.75 in equation(1)

$\begin{gathered} p+\text{3}(8.75)=30.50 \\ p+26.25=30.50 \\ p=30.50-26.25 \\ p=4.25 \end{gathered}$

The cost of a bucket of popcorn is $4.25

The cost of a fountain soda is $ 8.75