For a small party of 12 people the caterer offered a choice of a steak dinner for $12.00 per meal or a chicken dinner for $10.50 per meal. The final cost for the meals was $138.00. How many of each meal was ordered?

Question

Mathematics

Shane Lang

13 October, 08:04

For a small party of 12 people the caterer offered a choice of a steak dinner for $12.00 per meal or a chicken dinner for $10.50 per meal. The final cost for the meals was $138.00. How many of each meal was ordered?

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Cullen Ayala · Answer 1

Assuming one meal has been ordered for each person, let x and y represent the number of steaks and the number of chickens ordered, respectively. Then, we get the following system of linear equations. x + y = 12 (Eq. 1) 12x + 10.5y = 138 (Eq. 2) If we plug y = 12 - x, which is from Eq. 1, into Eq. 2, 12x + 10.5 (12 - x) = 138 1.5x + 126 = 138 1.5x = 12 x = 8 and plug x = 8 into Eq. 1, we get y = 4. So, they ordered 8 steaks and 4 chickens.