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22 January, 08:40

For a club gathering you were having, you bought a total of 50 burgers, and spent $90. You paid $2 per turkey burger, and $1.50 for each veggie burger. Next year, you want to spend the same amount of money on burgers, $90. If the number of turkey burgers is doubled, would you have to cut the number of veggie burgers in half? Explain your reasoning.

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  1. 22 January, 09:03
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    No. You would have to cut the number of veggie burgers in more than half.

    Explanation:

    1. Model the situation with a system of equations

    a) Name the variables:

    number of turkey burgers: t number of veggie burgers: v

    b) Number of burgers:

    50 = t + v

    c) Cost of the 50 burgers:

    $90 = 2t + 1.50v

    2. Solve that system of equations:

    a) System

    50 = t + v 90 = 2t + 1.50v

    b) Mutliply the first equation by 2 and subtract the second equation

    100 = 2t + 2v 90 = 2t + 1.50v

    10 = 0.5v v = 20 ⇒ t = 50 - 20 = 30

    c) How much would you spend if the next year you buy the double of 20 turkey burgers (40) and the half of 30 veggie burgers (15)

    $2 (40) + $1.50 (15) = $80 + $22.50 = $102.50

    Then, you if you double the number of turkey burgers, and cut the number burgers in half, you would spend more than $90 ($102.50).
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