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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.

Respuesta :

Edufirst

Answer:

  • 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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