At a sports performance center, Tara and Emek compared two training programs tested by groups of runners. Before training, Group A had an average endurance score of 80, while Group B averaged 84. After the first month, Program A increased its group's score by 15%, and the second month produced another 8% increase. Program B produced a 10% increase in the first month and another 12% increase in the second. Tara warned against simply adding each program's two percentage rates because the second change applied to the new score after the first month. For Group A, the final score was 80 x 1.15 x 1.08 = 99.36. For Group B, it was 84 x 1.10 x 1.12 = 103.488. Emek then compared overall growth relative to each starting value. Program A produced a 24.2% increase, while Program B produced a 23.2% increase. Although Group B finished with the higher endurance score, Program A produced the greater proportional growth. The coaches used that distinction to recommend Program A for athletes seeking the strongest relative improvement.

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Hint
After the first month, the second percentage increase uses a new, larger starting score.
Why is Program A's overall percentage increase greater than 15% + 8% = 23%?
Because the second 8% increase is applied to the higher score after the first-month increaseBecause 15% and 8% should always be multiplied to get the total percentage increaseBecause the original score of 80 must be added to both percentage ratesBecause every two consecutive percentage increases differ from their sum by exactly 1.2%
Correct. The second increase compounds on the score already increased by 15%.
Remember that the second month's percentage is applied to the first month's new score, not the original score.
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Hint
Multiply the starting score by 1.15 and then by 1.08.
Suppose another group starts with an endurance score of 100 and follows Program A, increasing by 15% in the first month and then 8% in the second month. What is its final endurance score? Please round it to the nearest integer.
Correct. The final score is 124.2, which rounds to 124 as a whole-number score.
Apply the two increases successively rather than simply adding 15 and 8 to the starting score.
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Hint
Compare each group's final score with its own starting score, not with the other group's starting score.
Group B finished with a higher score than Group A, but Program A produced greater proportional growth. Which statement best explains how both can be true?
Program B must have had the larger percentage increase because its final score was larger.Program A started from a lower score, so its smaller final score can still represent a larger percentage increase from its own starting value.Final scores and percentage growth are always unrelated.Program A had a higher second-month percentage, so the starting values do not matter.
Correct. A lower starting value can have a larger relative increase even if its final value remains lower.
Relative growth depends on change compared with each group's own starting value.
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Antrenman Programını Takip Etmek
TR
ARC_G12_FRD_02_STORY_02
Antrenman Programını Takip Etmek
Tracking the Training Program
EN
ARC_G12_FRD_02_STORY_02
Tracking the Training Program