Question

63 adults and 97 children attend, so the total projected cost of his meals is $4,169. Bonnie has 44 adults and 97 children on his guest list, so she will pay the caterer $3,409. How much does the caterer charge for each meal? Every adult's meal costs $ , and every child's meal costs $ .

Answer 1

To find the cost of adult and child meals, we set up two equations using the total costs and the number of meals. The elimination method is used to solve the system, yielding values for both the adult's meal (A) and the child's meal (C).

Step-by-step explanation:

We can approach this problem by setting up a system of linear equations. We'll assign the variable A to represent the cost of an adult's meal and the variable C to represent the cost of a child's meal. The given information allows us to formulate the following equations based on the total costs:

1. 63A + 97C = 4169 (the total cost for the number of adults and children attended)
2. 44A + 97C = 3409 (the total cost for Bonnie's guest list)

We can solve this system of equations using the method of substitution or elimination. Let's use the elimination method. We will multiply the second equation by 63/44 to align the coefficients of A in both equations.

Multiplying the second equation by 63/44 gives us:

1. 63A + 97C = 4169
2. (63/44)*44A + (63/44)*97C = (63/44)*3409

Simplifying the second equation, we get:

1. 63A + 97C = 4169
2. 63A + (63/44)*97C = 4786.75

Next, we subtract the first equation from the multiplied second equation to eliminate A:

1. (63A + 97C) - (63A + 97C) = 4169 - 4786.75

Which simplifies to:

0A + [(63/44)*97C - 97C] = -617.75

C can then be isolated to find the cost of a child's meal:

[(63*97 - 44*97)/44]C = -617.75
C = -617.75 / [(63*97 - 44*97)/44]

After calculating the value of C, we can substitute back into either equation to find the value of A.

After finding both A and C, we will have the cost of an adult's meal and a child's meal.