Question

At a lunch buffet, the price for an adult plate is $19, and the price for a child plate is $8. On Tuesday, a total of 32 plates were served, and the restaurant collected a total of $487 during the buffet. How many adult plates and child plates were sold?

Answer 1

Adult plate = 21 , child plate = 11

Explanation:

number of adult plate = a , no of child plate = c

$487 = $19a + $8c (equation 1)

32 = a + c (equation 2)

Multiply equation 2 by 8 gets you:

256 = 8a + 8c (equation 3)

Solve equation 1 and equation 3 simultaneously:

487 = 19a + 8c (equation 1) minus

256 = 8a + 8c (equation 3) :

231 = 11a

a = 231/11

a= 21

Substitute a = 21 into equation 2 :

32 = 21 + c

c = 32 - 21

c = 11

So 21 adult plates and 11 child plates were sold.

Answer 2

Explanation:

Number of children = c

Number of adults = a

Total number of adults & children = 32

c + a = 32 --------------------(I)

Total amount = $ 487

Cost of child plate = $8

Cost of c child plates = 8c

Cost of an adult plate = $19

Cost of a adult plate = 19a

8c + 19a = 487 ---------------(II)

Multiply equation (I) by (-8)

(I)* (-8) -8c - 8a = -256

(II) 8c + 19a = 487 {Now add & c will be eliminated}

11a = 231

a = 231/11

a = 21

Plugin the value of a in equation (I)

21 + c = 32

c = 32 - 21

c = 11

Number of adult plates = $ 21

Number of child plates = $ 11