Question

1. At a fundraiser breakfast, the bill for 3 glasses of orange juice and 5 pancake specials is $7.60, whereas the bill for 1 glass of orange juice and 2 pancake specials is $2.90. a. Write a system of 2 equations to model this problem. Let j stand for the price of a glass of juice and let p stand for the price of a pancake special. b. Use the substitution method to solve the system of equations. c. What would the bill be for 1 glass of orange juice and 1 pancake special?

Answer 1

A.
If:
j - the price of a glass of juice
p - the price of a pancake special
Then:
3j + 5p = 7.60
j + 2p = 2.90

b.
If:
j + 2p = 2.90
Then:
j = 2.90 - 2p
We can substite j in the first equation.
If:
3j + 5p = 7.60
j = 2.90 - 2p
Then: 
3×(2.90-2p) + 5p = 7.60
8.70 - 6p + 5p = 7.60
8.70 - p = 7.60
⇒ p = 8.70 - 7.60
⇒ p = 1.10

If:
j = 2.90 - 2p
p = 1.10
Then:
j = 2.90 - 2×1.10
j = 2.90 - 2.20
j = 0.70

Thus, the price of a glass of juice is $0.70 and the price of a pancake special is $1.10.

c.
If:
p = 1.10
j = 0.70
Then: 
j + p = 1.10 + 0.70 = 1.80

Thus, the bill for 1 glass of orange juice and 1 pancake special is $1.80.