Question

Gretchen has $50 that she can spend at the fair. Ride tickets cost $1.25 each and game

tickets cost $2 each. She wants to go on a minimum of 10 rides and play at least 12
games. Which system of inequalities represents this situation when r is the number of
ride tickets purchased and g is the number of game tickets purchased?
A. 1.25r + 2g <= 50 and r >= 10 and g >= 12
B. 1.25r + 2g >= 50 and r >= 10 and g > 12
C. 1.25r + 2g <= 50 and r > 10 and g >= 12
D. 1.25r + 2g >= 50 and r > 10 and g > 12

Answer 1

The correct system of inequalities for Gretchen's fair spending scenario is Option A: 1.25r + 2g ≤ 50 and r ≥ 10 and g ≥ 12, representing her budget limit and the desired minimum number of rides and games. The correct answer is option a.

Step-by-step explanation:

The system of inequalities that represents the scenario where Gretchen has $50 to spend at the fair, with ride tickets costing $1.25 each and game tickets costing $2 each, and her desire to go on a minimum of 10 rides and play at least 12 games needs to incorporate three inequalities:

1. Cost Inequality: The total cost of ride tickets (r) and game tickets (g) should not exceed Gretchen's budget of $50. Therefore, we have the inequality 1.25r + 2g ≤ 50.
2. Minimum Rides Inequality: Gretchen wants to go on at least 10 rides, which means the number of rides must be greater than or equal to 10. Hence, we have r ≥ 10.
3. Minimum Games Inequality: Similarly, she wants to play at least 12 games, leading to the inequality g ≥ 12.

Combining these inequalities, the correct system that describes this situation is:

A. 1.25r + 2g ≤ 50 and r ≥ 10 and g ≥ 12

This system of inequalities represents all the conditions given in Gretchen's scenario accurately. While she wishes to purchase a minimum number of each ticket, she does not wish to exceed her budget of $50, hence the ≤ (less than or equal to) sign in the cost inequality.