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10 January, 05:42

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.

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  1. 10 January, 06:09
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    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
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