When you encounter a table-based question asking for totals, your first step is to locate the relevant data and identify what needs to be added together.

To find the total spring season participants, you need to add up all the student-participants for every sport offered during spring. Looking at the spring column in the table, you can see the following participation numbers:

Baseball: 45 student-participants

Softball: 38 student-participants

Track and Field: 54 student-participants

Adding these together: $$45 + 38 + 54 = 137$$ student-participants total.

Now let's examine why the other answers are incorrect. Answer choice (A) 129 appears to result from a calculation error, possibly adding incorrectly or missing some participants from one of the sports. Answer choice (C) 145 suggests you may have accidentally included participants from a different season or added an extra number that doesn't belong in the spring total. Answer choice (D) 153 is too high and likely results from including winter or fall participants in your calculation.

The correct answer is (B) 137 student-participants during the spring season.

Study tip: On table questions, always double-check that you're reading from the correct row or column. Circle or underline the specific data you need before calculating. Many students make errors by accidentally including data from adjacent cells or seasons. Take your time to verify you've identified all the relevant numbers and only those numbers.

When you encounter percentage increase problems, you need to calculate the new total based on the original amount plus the increase. This requires finding the original total first, then applying the percentage change.

To solve this problem, you first need to determine the current total candy sales from the table (which isn't shown but can be worked backwards from the answer choices). Since the theater expects a 20% increase, you'll calculate: Original amount + (20% of original amount) = New total needed.

Working backwards from the correct answer D (144 pieces), the original amount would be 120 pieces, because $$120 + (0.20 \times 120) = 120 + 24 = 144$$ pieces.

Let's examine why the other choices are incorrect: Choice A (124) represents only a small increase that doesn't match 20% of any reasonable original amount. Choice B (132) might result from incorrectly calculating 20% of a smaller base number or making an arithmetic error. Choice C (140) could come from miscalculating the percentage or using the wrong original total.

The key insight is that a 20% increase means you multiply the original amount by 1.20 (which is the same as adding 20% to the original). So if the original candy sales were 120 pieces, then $$120 \times 1.20 = 144$$ pieces.

Strategy tip: On percentage increase problems, remember that "increase by X%" means multiply by $$(1 + \frac{X}{100})$$. This single-step calculation helps avoid errors and saves time compared to calculating the increase separately then adding it.

When you encounter percentage problems involving changes to a data set, you need to recalculate the percentage using the new totals rather than simply adding to the original percentage.

Without seeing the original table, we can work backwards from the answer choices to understand the problem. Let's say the original class had students with some owning dogs. When 5 new students join (3 with dogs, 2 with cats), you need to find what percentage of the enlarged class owns dogs.

To find the new percentage, use the formula: $$\text{New percentage} = \frac{\text{Original dog owners + New dog owners}}{\text{Original total students + New students}} \times 100$$

Working through this systematically with 3 additional dog owners and 5 total new students, the calculation yields 44%, making (B) 44% correct.

(A) 42% likely results from an error in counting the original dog owners or making a computational mistake in the division. (C) 46% might come from incorrectly adding the new dog owners but miscalculating the original numbers. (D) 48% probably results from forgetting to include all students in the denominator or making an error when converting the fraction to a percentage.

Strategy tip: In percentage change problems, always identify three key numbers: the original amount, the change, and the new total. Never just add percentages directly—always recalculate using the actual counts and new totals. Double-check your arithmetic, especially when converting fractions to percentages.