Multiple choice

Jane is playing a board game in which she must collect as many cards as possible. On her first turn, she loses $18$ percent of her cards. On the second turn, she increases her card count by $36$ percent. If her final card after these two turns is n, which of the following represents her starting card count in terms of n?

  1. $\dfrac{n}{(1.18)(0.64)}$
  2. $(1.18)(0.64)n$
  3. $\dfrac{n}{(1.36)(0.82)}$
  4. $(0.82)(1.36)n$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let X be starting count. X * (1 - 0.18) * (1 + 0.36) = n. X * 0.82 * 1.36 = n. X = n / (0.82 * 1.36).

AI explanation

Let the starting card count be x, which becomes 0.82x after an 18 percent loss. After increasing this amount by 36 percent, the final count is 0.82x multiplied by 1.36, which equals n. Solving for the starting card count x gives x equals n divided by the product of 1.36 and 0.82.

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