A gym offers 11 levels of fitnees classes, and in an attemp to reward those who progress...

BTGmoderatorLU wrote: ↑

Wed Apr 01, 2020 12:34 pm

Source: Veritas Prep

A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost for a course at the gym's highest level?

A. $175
B. $245
C. $425
D. $675
E. $725

The OA is A

Say the course fee for the first course = $x; thus the course fee for the second course = $(x – 50); thus the course fee for the third course = $(x – 50 – 50 = $(x – 2*50); thus the course fee for the fourth course = $(x – 3*50); ... the course fee for the sixth course = $(x – 5*50) = $(x – 250); ... the course fee for the 11th (highest level ) course = $(x – 10*50) = $(x – 500)

Since the course fees are equally spaced, the total course fee for all the 11 courses would be 11*Average course fee.

Average course fee = Median course fee; as the course fees are equally spaced

Median course fee = Course fee for the sixth course = $(x – 250)

Thus, total course fee = 11*$(x – 250) = 4,675

=> x = $675

Thus, the cost for a course at the gym's highest level (11th level) = $(x – 500) = $(675 – 500) = $175

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Wed Apr 01, 2020 12:34 pm

Source: Veritas Prep

A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost for a course at the gym's highest level?

A. $175
B. $245
C. $425
D. $675
E. $725

The OA is A

We can let x = the cost for a course at the highest level. Since that is the cheapest course, the cost for a course at the second highest level is x + 50, that at the third highest level is x + 100, and so on. Finally the most expensive course, which is at the lowest level, will cost x + 500. Therefore, we can create the equation:

x + (x + 50) + (x + 100) + … + (x + 500) = 4675

Notice there are 11 terms on the left hand side of the equation, and the terms are even spaced; therefore, we can use the formula for the sum of an evenly spaced set, which is average * quantity = sum. We note that the average of an evenly spaced set is found by the formula: (smallest value + largest value) / 2. Combining these two formulas, we can create the equation:

[x + (x + 500)]/2 * 11 = 4675

[2x + 500]/2 = 425

x + 250 = 425

x = 175

Answer: A