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.

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

Step-by-step 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