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.

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).