I am having a problem with word problems that are solving applied problems. Three equations.?

Starbucks sells cappuccinos in three sizes: tall for $2.65, grande for $3.20, and vente for $3.50. After a rally Bruce served 50 cappuccinos. The number of tall and vente cappuccinos, combined, was 2 fewer than the number of grande cappuccinos. If he collected a total of $157, how many cappuccinos of each size did he serve?

x=tall, y=grande, z=vente

1.) x + y + z = 50

2.) x + z = y - 2

I know 1.) is right, not sure about 2.), and I can't figure the third one.

Can anyone help me out?

5 Answers

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  • 1 decade ago
    Best Answer

    Your first two equations are correct.

    For the third equation, think of it this way:

    - How much does Bruce get for selling talls? 2.65*x.

    - How much does Bruce get for selling grandes? 3.20*y.

    - How much does Bruce get for selling ventes? 3.50*z.

    You know that the total amount of money collected is $157.

    Obviously, you get the total amount by adding up the amounts Bruce gets for selling talls, grandes, and ventes.

    Hence, your third equation is: 2.65x + 3.20y + 3.50z = 157.

    Hope that helps!

  • 1 decade ago

    1 and 2 are fine. the third should be

    2.65x + 3.20y + 3.50z = 157

    because you know the cost of each and the total amount collected. :)

  • 1 decade ago

    You are correct so far!

    The 3rd equation connecting x, y and z is

    $2.65x + $3.20y + $3.50z = $157

  • 1 decade ago

    2.65x + 3.20y + 3.50z = 157

    1st equation

    (x + z) = y - 2

    2nd equation

    x+ y + z = 50

    replace x and z

    ( x + z ) + y = 50

    y - 2 + y = 50

    2y - 2 = 50

    2y = 52

    y = 26

    plug in y

    2.65x + 3.2y + 3.5z = 157

    2.65x + 83.2 + 3.5z = 157

    2.65x +3.5z = 73.8

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  • Anonymous
    1 decade ago

    2.65x+3.20y+3.5z=157

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