Daniel had
4 and the rides cost $1.50 each, what is the greatest number of rides Daniel can go on? A. Write an inequality that represents Daniel’s situation. B. How many rides can Daniel go on?. Justify your an
The Correct Answer and Explanation is:
A. Inequality Representation:
Let xxx be the number of rides Daniel can go on. The cost of each ride is $1.50, and Daniel has $4. The total cost of xxx rides would be 1.50×1.50×1.50x, and the amount of money Daniel has is 4 dollars. To ensure that Daniel doesn’t spend more than his available money, the total cost must be less than or equal to 4. The inequality representing this situation is: 1.50x≤41.50x \leq 41.50x≤4
B. Solving the Inequality:
To find the greatest number of rides xxx, we need to solve the inequality: 1.50x≤41.50x \leq 41.50x≤4
- Divide both sides of the inequality by 1.50 to isolate xxx:
x≤41.50x \leq \frac{4}{1.50}x≤1.504
- Now, calculate the right-hand side:
x≤41.50=2.67x \leq \frac{4}{1.50} = 2.67x≤1.504=2.67
Since xxx represents the number of rides, and Daniel can’t go on a fraction of a ride, we round down to the nearest whole number. Therefore, the greatest number of rides Daniel can go on is: x=2x = 2x=2
Justification:
Daniel can afford 2 rides because the total cost for 2 rides is: 1.50×2=31.50 \times 2 = 31.50×2=3
This is less than or equal to his total amount of money, $4. If Daniel tries to go on 3 rides, the total cost would be: 1.50×3=4.501.50 \times 3 = 4.501.50×3=4.50
This exceeds his $4, so he cannot afford 3 rides. Therefore, the greatest number of rides Daniel can go on is 2.
