Manny and Zack are hosting events that are catered by the same company. Manny plans to have 66 adults and 27 children attend, so the total projected cost of his meals is $3,651. Zack has 77 adults and 43 children on his guest list, so he will pay the caterer $4,409. How much does the caterer charge for each meal?

The caterer charged $50 for an adult's meal and $13 for a child's meal

Step-by-step explanation:

Let the cost of an adult meal be $x

and the cost of a child meal be $y

From the question,

Manny plans to have 66 adults and 27 children and the total cost of his meals is $3,651.

We can write that

66x + 27y = 3651 (1)

Also, from the question,

Zack has 77 adults and 43 children and the total cost he will pay the caterer is $4,409.

We can also write that

77x + 43y = 4409 (2)

Multiply equation (1) by 7, so that we get

462x + 189y = 25557 (3)

Multiply equation (2) by 6, so that

462x + 258y = 26454 (4)

Now, subtract equation (3) from equation (4), so that

69y = 897

∴ y = 897/69

y = 13

Put the value of y into equation (1) to get x

66x + 27y = 3651

∴ 66x + 27(13) = 3651

66x + 351 = 3651

66x = 3651 - 351

66x = 3300

x = 3300/66

x = 50

Therefore,

The cost of an adult's meal is $50

and the cost of a child's meal is $13

Hence, the caterer charged $50 for an adult's meal and $13 for a child's meal.

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