Question

At a fundraiser breakfast, the bill for three glasses of orange juice and five pancake specials is $8.40, whereas the bill for one glass of orange juice and two pancake specials is $3.25. Write a system of two equations to model this problem. Let g stand for the price of a glass of juice and let p stand for the price of a pancake special. Use the method of your choice to solve the system of equations, What would be the bill for one glass of orange juice and one pancake special.

Answer 1

The bill for one glass of orange juice is $0.55 and the bill for one pancake special is $1.35

Explanation:

g stand for the price of a glass of orange juice

and let p stand for the price of a pancake special

According to question,

Statement 1: The bill for three glasses of orange juice and five pancake specials is $8.40

⇒ 3g + 5p = 8.40

Statement 2 : the bill for one glass of orange juice and two pancake specials is $3.25

⇒ g + 2p = 3.25

Thus our system of equation is

3g + 5p = 8.40 ........... (1)

g + 2p = 3.25 ........... (2)

Solving using elimiation method,

Multiply equation (2) by 3, we get,

3g + 6p = 9.75 ....(3)

Subtract equation (1) from (3), we get,

⇒ 3g + 6p -(3g +5p) = 9.75 - 8.40

⇒ 6p - 5p = 1.35

⇒ p = 1.35

Put p = 1.35 in (1),

3g + 5p = 8.40 ⇒3g + 5(1.35) = 8.40 ⇒ 3g = 8.40 - 6.75 ⇒ g = 0.55

Thus the bill for one glass of orange juice = $0.55 and the bill for one pancake special = $1.35