Movie Theatre word problem

Question

At the movie theatre, Mr. Smith bought his family 4 sodas and 3 popcorns for $27.25. Rick and his friends went to the same movie and they bought 5 sodas and 6 popcorns for $47.00. How much money does one soda cost? How much money does one popcorn cost?

Answer 1

Hy Thomas ,

 

Let's assign variables for sodas and popcorns. S for sodas and P for popcorns.

 

4s + 3p = 27.25

 

5s + 6p = 47.00

 

multiply the first equation by -2

 

-8s - 6p = -54.50

 

Now add the new equation with the second equation that you have above.

 

-3s = -7.50

 

s = 2.50

 

Now substitute this value for s into the first equation and find the value of p.

 

10 + 3p = 27.25

 

3p = 17.25

 

 

p = 5.75

 

One soda costs $2.50 and one  popcorn costs $5.75.

 

 

regards,

 

mayuran

 

 

Answer 2

Let S be the cost of one soda and P the cost of one popcorn.

4S + 3P = 27.25

5S + 6P = 47.00

 

Multiply the first equation by 2 and solve by elimination.

8S + 6P = 54.50

5S + 6P = 47.00   subtract

 

3S = 7.50

S= 2.50

 

Substitute for S in either equation and solve for P.

4(2.50) + 3P = 27.25

10 + 3P = 27.25

3P = 17.25

P = 5.75

 

Check:

4(2.50) + 3(5.75) = 27.25

10 + 17.25 = 27.25

27.25 = 27.25

5S + 6P = 47.00

5(2.50) + 6(5.75) = 47.00

12.50 + 34.50 = 47.00

47.00 = 47.00