Question

Jenny's volleyball team is hosting a dinner to raise money for new uniforms and equipment. The team's goal is to raise at least $1,100. A dinner ticket costs $20, and guests can also purchase raffle tickets for 50¢ apiece. If d represents the number of dinner tickets sold and r represents the number of raffle tickets sold, which inequality describes this situation? If the team sells 50 dinner tickets, how many raffle tickets does it need to sell?

Answer 1

Explanation:

20d + 0.5r >= 1100

in such an equation or inequality we need to relate the same things on both sides. we cannot mix apples and oranges. if we need to bring them together in one expression, we need to transfer them into a common attribute - like weight or (in this case) price.

so, our equality compares actually dollars : the dollars gained by selling tickets, and the total amount of dollars planned to earn ("at least" to create the inequality).

so, $20 per dinner ticket plus $0.50 per raffle ticket must be more than or equal to $1100.

now, for the situation that 50 dinner tickets have been sold (d = 50) we see

20×50 + 0.5r >= 1100

1000 + 0.5r >= 1100

0.5r >= 100

r >= 100/0.5 = 200

r >= 200

so, they need to sell at least 200 raffle tickets to reach the goal.