If 109 people attend a concert and tickets for adults cost $2.75 while tickets for children cost $2.25 and total receipts for the concert was $279.25, how many of each went to the concert?

Question

If 109 people attend a concert and tickets for adults cost $2.75 while tickets for children cost $2.25 and total receipts for the concert was $279.25, how many of each went to the concert?

Adults

Children

Tried this multiple times and kept getting it wrong :'(.

Answer 1

A = number of tickets sold to adults

C = number of tickets sold to children

Set up the system of linear equations based on the scenario.

2.75A + 2.25C = 279.25

A + C = 109

Use the substitution method: C = 109 - A

2.75A + 2.25(109 - A) = 279.25

2.75A + 245.25 - 2.25A = 279.25

0.5A + 245.25 = 279.25

0.5A = 34

A = 68

Plug in 68 for A to find C.

68 + C = 109 → C = 41

2.75(68) + 2.25(41) = 187 + 92.25 = 279.25

68 adults and 41 children went to the concert.