Answer: the systems of equations to solve the unit price of popcorn and rinks are
1 p + 3 d= 12.50---- equation 1
3 p + 4 d= 23.75 ---- equation 2
The price of A popcorn bucket = $4.25 and price of 1 fountain drink = $2.75
Step-by-step explanation:
Step 1
If p represents the number of popcorn buckets
and d represents the number of drinks,
The expression that Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50 becomes
1 p + 3 d= $12.50
and The expression that Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75 becomes
3 p + 4 d= $23.75
such that the systems of equations to solve the unit prices of popcorn and drinks are
1 p + 3 d= $12.50---- eqn 1
3 p + 4 d= $23.75 ---- eqn 2
Step 2
1 p + 3 d= $12.50---- eqn 1
3 p + 4 d= $23.75 ---- eqn 2
Multiplying equation 1 by( 3 )
1 p + 3 d= $12.50---- eqn 1 x 3
3p+ 9d= 37.5----- equation 3
and subtracting equation 2 from equation 3 becomes
3p+ 9d= 37.5----- equation 3
- 3 p + 4 d= $23.75
5d= 13.75
d= 13.75/5
d= 2.75
to find p, sinceaa d = 2.75,
1 p + 3 d= 12.50
1 p + 3 x 2.75= 12.50
p= 12.50-8.25
p=4.25
THerefore the price of popcorn = $4.25 and price of drinks = $2.75
