Word Problem dealing with money

Question

Adults' tickets for the art museum cost $1.50 more than children's tickets. One day 200 adults' tickets and 160 children's tickets were sold at the museum. The income from the adults' tickets was $30 more less than twice the income from the children's tickets. How much does each type of ticket cost?

Answer 1

We are given that the adult price is the children price plus $1.5

A = C + $1.50

 

Also one day the total adult price was 200(P_a) and the total children's price was 160(P_c)

The total adult price was twice the total children's price plus $30

200(A)= 2(160C) + 30

200(A) = 320(C) + 30

 

substituting (C + 1.5) for A from the first equation

 

200(C + 1.5) = 320(C) + 30

200(C) + 200(1.5) = 320(C) + 30

200(C) + 300 = 320(C) + 30

subtract 30 from both sides

200(C) + 270 = 320(C)

subtract 200(C) from both sides

270 = 120(C)

C = 2.25

A = C + 1.5

A = 3.75

 

Adult ticket price = $3.75

Child ticket price = $2.25