Chester has less than $25 to spend at the county fair

Question

Chester has less than $25 to spend at the county fair. The entrance fee is $5, and each ride costs $3. The number of rides, r, that Chester can go on is represented by the inequality 3r + 5 < 25. Select the most amount of rides Chester can go on without overspending

A: 4 

B: 6

C: 9 

D: 10

Answer 1

(Cost per ride)*(number of rides) + (entrance fee) < $25

                    3r                          +        5            < 25

 

     3r + 5 < 25

        3r < 20          [subtract +5 from both sides retains sense of inequality]

         r < 6  2/3      [divide both sides by +3 retains sense of inequality]

 

   Note: r must be a non-negative integer because it is the number of rides.

         r ≤ 6             [note: since 6 is ≤ 6 2/3]

 

"The most" means the largest possible integer value of r.

  Chester may take, at most, 6 rides without overspending.

 

Check:

    When taking 6 rides, Chester pays  $3*6+$5 = $23, which is less than $25.