Question

Your middle school is having a fall festival. Admission into the carnival is $3 and each game inside the carnival costs $.25. Write an inequality that represents the possible number of games that can be played having $10. What is the maximum number of games that can be played?

A). 0.25x + 3 < 10; 28 games

B). 0.25x + 3 is greater than or equal to 10; 28 games

C). 0.25x - 3 < 10; 52 games

D). 0.25x- 3 is greater than or equal to 10; 52 games

Answer 1

Answer: 0.25x + 3 ≤ 10; 28 games

Note how we have a "less than or equal to" sign, instead of simply a "less than" sign.

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Work Shown:

x = number of games

0.25x = amount spent on games only

0.25x+3 = total amount spent (games+admission)

total spent ≤ $10 since $10 is the most we have

0.25x + 3 ≤ 10 is the inequality we need to solve

0.25x ≤ 10-3 .... subtract 3 from both sides

0.25x ≤ 7

x ≤ 7/0.25 ............ divide both sides by 0.25

x ≤ 28

Since x is less than or equal to 28, this means the largest x can get is 28.

We can think of this as the ceiling value so to speak.

So the maximum number of games that can be played is 28.