Kamal had some apples. He sold 40% more apples than he ate. If he sold 70 apples, how many apples did he eat?

Introduction / Context:
This question involves a comparison between two related quantities using a percentage phrase, "40 percent more than." The number of apples sold is described as being 40 percent more than the number eaten. We are given the number sold and must find how many were eaten. This is a simple algebraic application of percentage increase, reinforcing how to translate verbal relationships into equations.

Given Data / Assumptions:
Let the number of apples Kamal ate be A.
He sold 40 percent more apples than he ate.
Number of apples sold = 70.
We assume that "40 percent more than A" means A plus 40 percent of A.

Concept / Approach:
If one quantity is 40 percent more than another quantity A, then it is A + 40 percent of A = A + 0.40A = 1.40A. In this problem, the number sold equals 1.40 times the number eaten. Since the number sold is given as 70, we can write the equation 1.40A = 70 and solve for A. This kind of direct proportional equation is straightforward once the verbal phrase is converted into algebraic form.

Step-by-Step Solution:
Let the number of apples eaten by Kamal be A. He sold 40 percent more apples than he ate. So, apples sold = A + 40 percent of A = A + 0.40A = 1.40A. We are given that apples sold = 70. Therefore, 1.40A = 70. To find A, divide both sides by 1.40: A = 70 / 1.40. Compute 70 / 1.40 = 50. Thus, Kamal ate 50 apples.

Verification / Alternative check:
We can verify by checking the percentage relationship. If Kamal ate 50 apples, then 40 percent of 50 is 0.40 * 50 = 20. He sold 50 + 20 = 70 apples. This matches the given number sold, confirming that 50 is correct. Any other assumed number of apples eaten would not yield exactly 70 when increased by 40 percent.

Why Other Options Are Wrong:
If he had eaten 18 apples, then apples sold would be 1.40 * 18 = 25.2, not 70. If he had eaten 42 apples, apples sold would be 1.40 * 42 = 58.8, again not 70. If he had eaten 90 apples, apples sold would be 1.40 * 90 = 126, which is much higher than 70. Only 50 apples eaten leads to exactly 70 apples sold with the given 40 percent more condition.

Common Pitfalls:
A recurring mistake is to interpret "40 percent more than" as simply 40 percent of the quantity, rather than 140 percent of it. Another error is to subtract 40 percent instead of adding it, which would incorrectly model a decrease. Some students also misplace the percentage base, taking 40 percent of 70 instead of 40 percent of the eaten quantity. Carefully translating verbal descriptions into the correct algebraic form is essential to avoid these mistakes.

Final Answer:
Kamal ate 50 apples.