Question

A basketball team sells tickets that cost​ $10, $20,​ or, for VIP​ seats,​ $30. The team has sold 3192 tickets overall. It has sold 179 more​ $20 tickets than​ $10 tickets. The total sales are ​$61,630. How many tickets of each kind have been​ sold?

A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3192 tickets overall. It has sold 179 more $20 tickets than $10 tickets. The total sales are $61,630. How many tickets of each kind have been sold? How many $10 tickets were sold? How many $20 tickets were sold? How many $30 tickets were sold?

Answer 1

Given, A basketball team sells tickets that cost $10, S20, or, for VIP seats, S30. Let the number of seats be a, b, c with cost 10, 20, 30 respectively The team has sold 3192 tickets overall. atbtc 3192 It has sold 179 more $20 tickets than $10 tickets. 179+a-b The total sales are S61,630. 10a+20b+30c 61630 equations are a+b-c 3192 179+a b 10a+20b+30c 61630

Substituting equation 2 in 1,3 which results in 2a-c= 3013 4 30a +30 c 58050 which implies a + c 1935 5 Solving equation 4,5 a-1078, c-857 Substituting these values in equation l, we get b-1257 S10 tickets are 1078 $20 tickets are 1257 S30 tickets are 857