Daniela, Kieu, and Cameron decide to go to the movies one hot summer afternoon. The theater is having a summer special called Three Go Free. They will get free movie tickets if they each buy a large popcorn and a large soft drink. They take the deal and spend a total of $22.50 on large popcorns and soft drinks. The next week, they go back again, only this time, they each pay $8 for a ticket, they each get a large soft drink, but they share one large bucket of popcorn. This return trip costs them a total of$37.50. Use systems of equations to find the price of a large soft drink and the price of a large bucket of popcorn!

Price of a large soft drink = $3

Price of large bucket of popcorn = $4.5

Step-by-step explanation:

Let the cost of one large popcorn = $P

And the cost of one large soft drink = $S

If Daniela, Kieu and Cameron avail the deal of Three Go Free,

3P + 3S = 22.50

P + S = 7.5 (1)

Next time they each pay $8 for a ticket, they each get a large soft drink but they share one large bucket of popcorn.

This trip cost them = $37.50

Cost of 3 tickets + Cost of 3 large soft drinks + Cost of one large bucket of popcorn = 37.50

(3 × 8) + (3 × S) + P = 37.5

24 + 3S + P = 37.5

3S + P = 13.5 (2)

By subtracting equation (1) from equation (2),

(3S + P) - (P + S) = 13.5 - 7.5

2S = 6

S = $3

From equation (1),

P + 3 = 7.5

P = $4.5

Therefore, price of a large soft drink is $3 and a large bucket of popcorn is $4.5

468

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have