Final answer:
To determine the highest number of new uniforms the cheerleaders can purchase, the inequality 500 - 50u <= 1500 must be correctly interpreted and solved for 'u'. The correct operational steps reveal that the maximum number of uniforms that can be purchased is 10 uniforms (option a).
Step-by-step explanation:
To find the highest number of new uniforms the cheerleaders can purchase using the inequality 500 - 50u = 1500, let's solve for 'u' which represents the number of uniforms.
First, we need to get 'u' by itself on one side of the equation. Here are the steps:
- Subtract 500 from both sides:
500 - 50u - 500 = 1500 - 500 - Simplify:
-50u = 1000 - Divide both sides by -50 to solve for 'u':
u = 1000 / -50
Simplify:
u = -20
However, since we cannot have a negative number of uniforms, and we are dealing with an inequality, we must have made a mistake. We should be looking at the inequality sign carefully. The correct setup should've been 500 - 50u <= 1500 (less than or equal to), rather than an equals sign. Let's correct the process:
- Subtract 500 from both sides:
500 - 50u - 500 <= 1500 - 500 - Simplify:
-50u <= 1000 - Divide both sides by -50, and remember to flip the inequality sign:
u <= -20
Now, the inequality u <= -20 still does not make sense as we cannot purchase a negative number of uniforms. Thus, it seems we have an incorrect inequality to begin with. Since purchasing uniforms should reduce the total funds, the inequality for the funds remaining after purchasing uniforms should be greater than or equal to zero. Correcting the inequality again to 500 - 50u >= 0, we get:
- Subtract 500 from both sides:
500 - 50u - 500 >= 0 - 500 - Simplify:
-50u >= -500 - Divide both sides by -50, and flip the inequality sign because we divided by a negative:
u <= 10
Therefore, the highest number of new uniforms the cheerleaders can purchase is 10 uniforms, which is option (a).