Question

Sophia spends a total of $20.50 on 4 bags of popcorn and 2 drinks. Sophie spends a total of $34.50 on 6 bags of popcorn and 4 drinks. Write a system of equations

Answer 1

Answer:

4p+2d=20.5

6p+4d=34.50

popcorn cost: 3.25

drink cost: 3.75

Step-by-step explanation:

1) Assigning a variable

p=popcorn

d=drinks

2) Writing the system of equations

4p+2d=20.5

6p+4d=34.50

3) Simplifying one equation

2d=20.5-4p

d=10.25-2p

4) Substitution

6p+4d=34.5

6p+4(10.25-2p)=34.5

6p+41-8p=34.5

-2p+41=34.5

-2p=-6.5

p=3.25

5) Finding d

d=10.25-2(3.25)

d=10.25-6.5

d=3.75