MATH SOLVE

4 months ago

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

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