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)β-6S-12L=-93
Multiplying the second equation by (4): (2) (4)(5S+3L=35.5)β20S+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