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Does anyone know how to do this math word problem?

For his team popcorn fundraiser sale, Maike sold caramel corn for $10, buttered microwave popcorn for $8, and lightly buttered microwave popcorn for $7. By the end of the fundraiser, he had sold 400 items and made $3,272. If he sold twice as many lightly buttered microwave popcorn boxes as the buttered popcorn, how many of each type of popcorn did he sale?

Let C = Caramel Popcorn
Let B = Buttered Popcorn
Let L = Lightly Buttered Popcorn

(1) C + B + L = 400
(2) 10C + 8B + 7L = 3272
(3) L = 2B

Substitute L = 2B from Equation 3 into Equation 1:

C + B + 2B = 400

(1a) C + 3B = 400

Substitute L = 2B from Equation 3 into Equation 2:

10C + 8B + 14B = 3272

(2a) 10C + 22B = 3272

Multiply Equation 1a by 10:

(1b) 10C + 30B = 4000

Subtract Equation 2a from Equation 1b:

(10C – 10C) + (30B – 22B) = (4000 – 3272)

8B = 728

B = 91

Substitute B = 91 into Equation 3:

L = 2B

L = 2 * 91

L = 182

Substitute B = 91 and L = 182 into Equation 1:

C + B + L = 400

C + 91 + 182 = 400

C = 127

CHECK:

(1) C + B + L = 400 —> 127 + 91 + 182 = 400 —> 400 = 400 CHECK

(2) 10C + 8B + 7L = 3272 —> 1270 + 728 + 1274 = 3272 —> 3272 = 3272 CHECK

(3) L = 2B —> 182 = 2 * 91 —> 182 = 182 CHECK

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