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).