Assuming each guest will eat only one serving of dessert, how many of each dessert should he make?

Question

Thomas is making cheesecakes and chocolate pies. Each cheesecake serves twelve people and costs $10 to make. Each chocolate pie serves eight and costs $6 to make. He needs to serve 88 people on a budget of $70. Assuming each guest will eat only one serving of dessert, how many of each dessert should he make?

Answer 1

Let;

 

C = number of Cheesecakes to make

P = number of Pies to make

 

Equation 1: account for number of guests

 

Each cheesecake serves 12 people, each pie serves 8 for a total of 88 guests.

 

12C + 8P = 88

 

Equation 2: Account for cost $$

 

Cheesecake cost 10$ to make, Pie cost 6$ on a 70$ budget.

 

10C + 6P = 70

 

Now we have ;

 

Eq. 1)

12C + 8P = 88

 

rearrange using algebra

 

8P = 88 - 12C

P = 88/8 - (12/8)C

P = 11 - 1.5C

 

Substitute this into Eq. 2 for P

 

Eq. 2)

10C + 6P = 70

10C + 6(11 - 1.5C) = 70

10C + 66 - 9C = 70

C + 66 = 70

C = 70 - 66

C = 4

 

Plug C = 4 into either equation to find P, the number of pies needed.

 

10C + 6P = 70

10(4) + 6P = 70

40 + 6P = 70

6P = 30

P = 5