Question

Julio and his friends go to the movies on 3 different nights . The first night they purchase 4 bags of popcorn and 6 sodas at a cost of 32.70 . The second night, they purchased 2 bags of popcorn and 4 sodas at a cost of 19.30 . On the third night, if they wanted to buy 3 bags of popcorn and 4 sodas, how much will it cost .

Answer 1

Answer

The answer is that is would cost $  to buy 3 bags of popcorn and 4 sodas.

Step-by-step explanation:

To answer this question you will set up a system of equations to represent each scenario.  Solve for one variable and substitute that in to the other equation to find the missing value.  This example will have you solving for p, the price of popcorn or s for the price of soda.

The equation for the first night would look like where p is popcorn and s is soda:

4p + 6s = 32.70

The equation for the second night would look like where p is popcorn and s is soda:

2p + 4s = 19.30

so first you'd solve the first equation and it would look like this:

4p + 6s = 32.70

-4p       -4p         *minus 4p from both sides*

6s = -4p + 32.70

/6       /6              *divided by 6 on both sides*

s = 5.45 − 2/3p

Then put (-2/3p + 5.45) into the second equation for S. Then solve which will look like this:

2p + 4 (−2/3p + 5.45)

2p − 8/3p + 21.8 = 19.3

*To write 2p as a fraction with a common denominator, multiply by

3/3*

2p ⋅ 33 − 8/3p + 21.8 = 19.3

*simplify terms*

2p ⋅ 3 - 8/3p + 21.8 = 19.3

−2/3p + 21.8 = 19.3

          - 21.8   - 21.8

-2/3p = -2.5

/(-2/3)   /(-2/3)

p = 3.5  

The price of popcorn is 3.50 and the soda is  5.45 − 2/3(3.5) *filling in 3.50 for P* which equals 3.11

So 3 bags of popcorn and 4 sodas will cost 22.94.

my answer my not be right but the process is. so try to go through it yourself.