At an athletics training center, Tara and Emek studied a data panel showing an athlete's weekly training load of 750 units. The coach planned to increase the load by 16 percent for the next week, but the athlete's recovery score remained low. Under the training plan, a low score required a 10 percent reduction from the increased load. Tara first calculated 750(1.16) = 870 units. Emek then applied the reduction to this new amount: 870(0.90) = 783 units. The coach initially wondered whether a 16 percent increase followed by a 10 percent decrease meant a net increase of 6 percent. Tara explained that the percentages were based on different amounts. Their calculation showed that 783 units was actually 33 units above the original 750, an overall increase of 4.4 percent. After checking the successive multipliers, they recommended a target of 783 units. The coach accepted the adjusted plan, balancing increased training with the athlete's need for recovery.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Represent each percentage change with its own multiplier and apply the changes successively.
Which calculation correctly represents the 16 percent increase followed by the 10 percent reduction in the training plan?
750(1 + 0.16 - 0.10)750(1.16)(0.90)750(0.16)(0.10)750(1.16)(1.10)
Correct. The increase uses a multiplier of 1.16, and the following reduction uses a multiplier of 0.90.
Not quite. The two percentage changes are applied one after the other to different amounts.
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Hint
A 6 percent increase corresponds to multiplying the original load by 1.06.
The coach incorrectly treats the 16 percent increase and 10 percent decrease as a net increase of 6 percent. How many units would this incorrect method give for the original training load of 750 units?
Correct. A 6 percent increase on 750 units would give 795 units.
Check the amount obtained by increasing 750 by 6 percent.
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Hint
Identify the amount used as the base for each percentage change.
Why does a 16 percent increase followed by a 10 percent decrease produce an overall increase of 4.4 percent rather than 6 percent?
Because percentage decreases must always be doubled when they follow an increase.Because 16 percent and 10 percent cannot be used with decimal multipliers.Because the 10 percent reduction is taken from the increased load of 870 units, not from the original 750 units.Because the 16 percent increase should have been calculated from 783 units.
Correct. The second percentage is applied to the new amount, so the two percentage changes cannot simply be subtracted.
Not quite. Focus on which training load serves as the base for the 10 percent reduction.
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Antrenman Yükü Kararı
TR
ARC_G11_FRD_02_STORY_03
Antrenman Yükü Kararı
The Training Load Decision
EN
ARC_G11_FRD_02_STORY_03
The Training Load Decision