A soccer player practices for at least 16 hours per week, and each practice lasts for three-fourths of an hour. If she has already practiced for 4 hours this week, how many more times does she need to practice for her to meet or exceed her weekly goal?
A. r ≥ 6 times
B. r ≥ 15 times
C. r ≥ 16 times
D. r ≥ 27 times
Answer (2)
Define x as the number of additional practices.
Set up the inequality: 4 + 4 3 x ≥ 16 .
Solve for x : x ≥ 16 .
The soccer player needs to practice at least 16 more times: x ≥ 16
Explanation
Setting up the Inequality Let x be the number of additional practices needed. The total practice time will be the sum of the time already practiced and the time from additional practices. We need to set up an inequality where the total practice time is greater than or equal to 16 hours.
The Inequality The inequality is: 4 + 4 3 x ≥ 16
Isolating the Variable Subtract 4 from both sides of the inequality: 4 3 x ≥ 16 − 4 4 3 x ≥ 12
Solving for x Multiply both sides by 3 4 to solve for x : x ≥ 12 × 3 4 x ≥ 3 48 x ≥ 16
Conclusion Therefore, the soccer player needs to practice at least 16 more times to meet or exceed her weekly goal.
Examples
Understanding inequalities is crucial in various real-life scenarios. For instance, if you're managing a budget and need to ensure your expenses don't exceed your income, you use inequalities to set limits and make informed decisions. Similarly, in cooking, you might need to adjust ingredient quantities to stay within a certain range for a recipe to turn out correctly. Inequalities help us define boundaries and make sure we stay within acceptable limits in many practical situations.
The soccer player needs to practice at least 16 more times to meet her weekly goal of practicing for at least 16 hours. This is derived from the equation relating her current practice time and the time needed from additional practices. Therefore, the answer is r ≥ 16 times .
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