Question

If 112 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $and total receipts for the concert was $231.00, how many of each went to the concert?

Answer 1

70 adults

42 children

Explanation:

A + C = 112

A = 112 - C

2.25A + 1.75C = 231

2.25(112 - C) + 1.75C = 231

252 - 2.25C + 1.75C = 231

21 = 0.5C

C = 42

A = 112 - C

A = 112 - 42

A = 70

Answer 2

42 child and 70 adult

Explanation:

Let a = number of adult tickets

c = number of child tickets

a+c = 112

2.25a + 1.75c = 231

Solve the first equation for a

a = 112-c

Substitute this into the second equation

2.25(112-c) + 1.75c = 231

Distribute

252 - 2.25c +1.75c = 231

Combine like terms

252 -.5c = 231

Subtract 252 from each side

252-252 -.5c = 231-252

-.5c = -21

Divide each side by -.5

-.5c/-.5 = -21/ -.5

c = 42

Now can find a

a = 112-c

a = 112-42

a = 70