Question

You and your friends get to go to an amusement park. You have $75 for the day. The entrance fee is $49.95 and lunch is $11. You want to be able to join your friends and play in the arcade. Each game is $1.75.

a. Write an inequality to express the number of games you can play.
b. How many games can you play? Graph the solution interval on a number line on a sheet of paper. Describe how your graph looks.
c. After you have played in the arcade, have you spent all your money? If not, how much is left over? Explain your answer.
d. If you want to play 2 more games to beat your record, how much less will your lunch need to cost?

Answer 1

a) each game is $1.75. for (x) games, the cost is therefore 1.75*x. Add this onto the entry fee and cost of lunch to get the total amount paid. Set the total less than/equal to the total amount, 75.

Answer 2

b) solve the inequality for x. Note: if you get a non-integer, you need to round down to the nearest whole number. For example, if you get x <= 5.5, you can only afford 5 games, not 6, so you need to round down.

Answer 3

c) take the maximum x value allowed by your inequality, calculate the cost of x games (1.75x), add on the entry and lunch fees. Is it exactly 75? Or is it less than 75, and if so, how much less?

Answer 4

d) take the leftover amount from 75 (if any)

Multiply 2*1.75 to get the cost of two more games

Subtract (cost of two games - leftover money) to get the $ needed