a Set up two equations, one describing the first movie night and another describing the second movie night.
B
b Could you do a graphing approach?
A
aLarge Drink: $3
Large Popcorn: $4.5
B
b See solution.
Practice makes perfect
a We have two unknowns, the price for a large popcorn and the price for a large drink. We already know the price for a ticket. Let's introduce some variables.
Large popcorn&= P
Large drink&= D
Ticket price&= $ 8
The first time at the movies, the tickets were free. However, they bought 3 large popcorns and 3 large drinks totaling $22.50. This can be written as the following equation.
3P+3D=22.5
The next time they visit the movies, they buy one large popcorn, 3 large drinks and 3 tickets. This can be written as a second equation.
P+3D+3(8)=37.5
If we combine these equations, we can write a system of equations which we can solve with the Elimination Method.
A large drink costs $3 and a large popcorn costs $4.5.
b We used a system of equations. An alternative method could be to graph the equations. This would require us to first write them in slope-intercept form.
3P+3D=22.50 P+3D+24=37.5
⇓
P=7.5-D P=13.5-3D
If we graph these equations, their point of intersection will tell us how much a large popcorn and a large drink costs. Notice that neither item can have a negative price and therefore, they are limited to non-negative values.
