On the annual day of a school sweets are to be distributed equally among 112 children. On that day 32 children are absent, so each of the remaining children receives 6 extra sweets. How many sweets was each child originally supposed to get?

Introduction:
This question is a classic example of how absence of some members changes the distribution when a fixed total quantity is shared equally. The key is to express the total number of sweets in terms of the original per child share and then relate it to the increased share when fewer children are present.

Given Data / Assumptions:
- Total number of children initially planned for distribution = 112. - On the actual day, 32 children are absent. - Therefore, number of children present = 112 - 32 = 80. - Each present child receives 6 sweets more than originally planned. - We must find the original number of sweets per child.

Concept / Approach:
Let the original number of sweets per child be x. Then the total number of sweets is 112x. When only 80 children are present, these same 112x sweets are redistributed so that each present child gets x + 6 sweets. Equating the two expressions for total sweets leads to an equation in x which we can solve.

Step-by-Step Solution:
Step 1: Let the original number of sweets that each child was supposed to receive be x. Step 2: Then total number of sweets = 112x. Step 3: On the day of distribution, number of children present = 112 - 32 = 80. Step 4: Each present child now receives x + 6 sweets. Step 5: Total sweets distributed to the present children = 80 * (x + 6). Step 6: The total number of sweets is the same whether all 112 children are present or only 80 are present. Step 7: Therefore, 112x = 80(x + 6). Step 8: Expand the right side: 112x = 80x + 480. Step 9: Subtract 80x from both sides: 112x - 80x = 480 gives 32x = 480. Step 10: Solve for x: x = 480 / 32 = 15.

Verification / Alternative Check:
If each child was originally supposed to get 15 sweets, the total sweets = 112 * 15 = 1680. On the actual day, with 80 children present, each child receives 15 + 6 = 21 sweets. The total sweets distributed now are 80 * 21 = 1680, which matches the original total. This confirms that the value x = 15 is correct.

Why Other Options Are Wrong:
Options 12, 14, 16 and 18 do not satisfy the equation 112x = 80(x + 6). Substituting any of these values for x leads to unequal totals on both sides.

Common Pitfalls:
Students sometimes incorrectly set up the equation or forget that the total number of sweets remains fixed. Another common error is miscomputing 80(x + 6) or making arithmetic mistakes when simplifying 32x = 480. Writing all steps clearly helps avoid these mistakes.

Final Answer:
Each child was originally supposed to get 15 sweets.