Nasir bought 9 storage bins that were each the same price. He used a coupon for $63 off the entire...

1. TRANSLATE the problem information

• Given information:
  • 9 storage bins, each the same price
  • \(\$63\) coupon used on entire purchase
  • Final cost after coupon = \(\$27\)
  • Need to find: original price for 1 bin

2. INFER the approach

• Key insight: The coupon was subtracted from the original total to get \(\$27\)
• Strategy: Work backwards - add the coupon amount back to find the original total, then divide by 9

3. SIMPLIFY to find original total cost

• Original total = Final cost + Coupon amount
• Original total = \(\$27 + \$63 = \$90\)

4. SIMPLIFY to find price per bin

• Price per bin = Total cost ÷ Number of bins
• Price per bin = \(\$90 \div 9 = \$10\)

Answer: 10

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what the \(\$63\) coupon means and subtract it from \(\$27\) instead of adding it back.

They might calculate: \(\$27 - \$63 = -\$36\), leading to confusion about negative costs, or they might think the original price per bin is \((\$27 - \$63) \div 9\), which creates nonsensical negative results. This leads to confusion and guessing.

Second Most Common Error:

Incomplete SIMPLIFY execution: Students correctly find that the original total was \(\$90\) but make an arithmetic error when dividing by 9.

They might calculate \(90 \div 9\) incorrectly, perhaps getting \(\$9\) or \(\$11\) due to rushing through the division. This leads to selecting an incorrect answer choice if those values are among the options.

The Bottom Line:

This problem tests students' ability to work backwards through a discount scenario - the key insight is recognizing that to "undo" a coupon, you must add its value back to the final cost.