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?

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.