Q:

there are two different sized drinks sold at a local movie theater a family bought two small drinks in 4 large drinks for $31 a group of students bought five small drinks and three large drinks for $35.50 how much is a small drink

Accepted Solution

A:
Price of a small drink: S
Price of a large drink: L

A family bought two small drinks in 4 large drinks for $31:
(1) 2S+4L=31

A group of students bought five small drinks and three large drinks for $35.50:
(2) 5S+3L=35.5

how much is a small drink:
S=?

We have a system of two equations and two unkowns:

(1) 2S+4L=31
(2) 5S+3L=35.5

Using the reduction's method:
Multiplying the first equation by (-3):
(1) (-3)(2S+4L=31)→-6S-12L=-93

Multiplying the second equation by (4):
(2) (4)(5S+3L=35.5)→20S+12L=142

Adding the two equations:
-6S-12L+20S+12L=-93+142
14S=49
Solving for S. Dividing both sides of the equation by 14:
14S/14=49/14
S=3.50

Answer: A small drink costs $3.50 each one