At a recent sale, Harue bought various numbers of 5 types of school supplies - markers, pens, pencils, erasers, and...

1. Translate the problem requirements: Convert each pricing deal into its equivalent discount percentage to identify which one matches the "Buy one, get one at 50% off" promotion
2. Calculate the effective discount for each supply type: For each deal, determine what percentage discount Harue receives compared to regular pricing
3. Identify the target discount pattern: Determine what effective discount "Buy one, get one at 50% off" actually provides
4. Match the calculated discounts: Compare each supply's effective discount to the target pattern to find the match

Execution of Strategic Approach

1. Translate the problem requirements

Let's start by understanding what "Buy one, get one at 50% off" actually means in everyday terms. When you buy two items under this promotion, you pay full price for the first item and half price for the second item. So for 2 items, you pay \(1 + 0.5 = 1.5\) times the regular price instead of 2 times the regular price. This means you're getting a discount.

To find the discount percentage: You save 0.5 out of every 2 regular prices, which is \(\frac{0.5}{2} = 0.25\) or 25% off the total.

So we need to find which school supply gives Harue an effective 25% discount.

Process Skill: TRANSLATE - Converting the "buy one, get one at 50% off" language into a concrete discount percentage

2. Calculate the effective discount for each supply type

Now let's look at each deal and figure out what discount Harue actually gets:

Markers: "4 for the price of 3"

• Harue gets 4 markers but only pays for 3
• She saves the cost of 1 marker out of 4
• Discount = \(\frac{1}{4} = 0.25 = 25\%\)

Pens: "3 for the price of 2"

• Harue gets 3 pens but only pays for 2
• She saves the cost of 1 pen out of 3
• Discount = \(\frac{1}{3} ≈ 0.33 = 33\%\)

Pencils: "5 for the price of 3"

• Harue gets 5 pencils but only pays for 3
• She saves the cost of 2 pencils out of 5
• Discount = \(\frac{2}{5} = 0.40 = 40\%\)

Erasers: "2 for the price of 1"

• Harue gets 2 erasers but only pays for 1
• She saves the cost of 1 eraser out of 2
• Discount = \(\frac{1}{2} = 0.50 = 50\%\)

Notebooks: "5 for the price of 2"

• Harue gets 5 notebooks but only pays for 2
• She saves the cost of 3 notebooks out of 5
• Discount = \(\frac{3}{5} = 0.60 = 60\%\)

3. Identify the target discount pattern

From step 1, we determined that "Buy one, get one at 50% off" provides an effective discount of 25% off the total purchase.

4. Match the calculated discounts

Comparing our calculated discounts to the target 25% discount:

• Markers: 25% ✓ (This matches!)
• Pens: 33%
• Pencils: 40%
• Erasers: 50%
• Notebooks: 60%

Only the markers deal gives exactly 25% off, which matches the "Buy one, get one at 50% off" promotion.

Final Answer

The answer is A. Markers. The "4 for the price of 3" deal on markers is equivalent to a "Buy one, get one at 50% off" promotion, as both provide an effective 25% discount.

Common Faltering Points

Errors while devising the approach

Faltering Point 1: Misinterpreting "Buy one, get one at 50% off"
Many students incorrectly assume this means a 50% discount on the total purchase. However, it actually means you pay full price for the first item and half price for the second item, resulting in paying 1.5 times the regular price for 2 items instead of 2 times, which equals a 25% discount overall.

Faltering Point 2: Not recognizing the need to calculate effective discount percentages
Students might try to directly match the verbal descriptions (like "4 for 3") without converting each deal into its equivalent discount percentage. This makes comparison impossible since the target promotion is described differently.

Errors while executing the approach

Faltering Point 1: Calculating discount percentage incorrectly
For deals like "4 for the price of 3," students might calculate the discount as \(\frac{3}{4} = 75\%\) (what you pay) instead of \(\frac{1}{4} = 25\%\) (what you save). The discount should always be (amount saved)/(total regular price).

Faltering Point 2: Arithmetic errors in fraction-to-percentage conversion
When converting fractions like \(\frac{1}{3}\), \(\frac{2}{5}\), or \(\frac{3}{5}\) to percentages, students may make basic arithmetic mistakes, leading to incorrect discount calculations that don't match the target 25%.

Errors while selecting the answer

Faltering Point 1: Selecting the wrong matching discount
Even after calculating all discounts correctly, students might accidentally select a deal with a different discount percentage (like 33% or 40%) instead of the one that exactly matches 25%, possibly due to rushing or misreading their own calculations.

Alternate Solutions

Smart Numbers Approach

Step 1: Assign smart number for regular price
Let's assume each item normally costs $10 (chosen because it makes percentage calculations straightforward).

Step 2: Calculate what "Buy one, get one at 50% off" means
For 2 items: Pay \(\$10 + \$5 = \$15\) instead of $20
Savings = $5 out of $20 = 25% total discount
This means getting 2 items for the price of 1.5 items.

Step 3: Calculate effective pricing for each supply type

Markers: 4 for the price of 3
Pay: \(3 \times \$10 = \$30\)
Regular cost: \(4 \times \$10 = \$40\)
Savings: $10 out of $40 = 25% discount ✓

Pens: 3 for the price of 2
Pay: \(2 \times \$10 = \$20\)
Regular cost: \(3 \times \$10 = \$30\)
Savings: $10 out of $30 = 33.3% discount

Pencils: 5 for the price of 3
Pay: \(3 \times \$10 = \$30\)
Regular cost: \(5 \times \$10 = \$50\)
Savings: $20 out of $50 = 40% discount

Erasers: 2 for the price of 1
Pay: \(1 \times \$10 = \$10\)
Regular cost: \(2 \times \$10 = \$20\)
Savings: $10 out of $20 = 50% discount

Notebooks: 5 for the price of 2
Pay: \(2 \times \$10 = \$20\)
Regular cost: \(5 \times \$10 = \$50\)
Savings: $30 out of $50 = 60% discount

Step 4: Match the target discount
Only markers provide exactly 25% discount, which matches "Buy one, get one at 50% off."

Answer: A. Markers