An outdoor stage must be 130 centimeters tall. The base platform contributes 10 centimeters of height. The remaining height is...

1. TRANSLATE the problem information

• Given information:
  • Total stage height needed: \(\mathrm{130\text{ cm}}\)
  • Base platform height: \(\mathrm{10\text{ cm}}\)
  • Short riser blocks: \(\mathrm{6\text{ cm}}\) each, x blocks used
  • Tall riser blocks: \(\mathrm{8\text{ cm}}\) each, y blocks used

2. INFER the relationship

• The total height must equal the sum of all height contributions
• Total height = Base platform + All short blocks + All tall blocks
• We need: \(\mathrm{130 = 10 + 6x + 8y}\)

3. TRANSLATE this into standard equation form

• Starting with: \(\mathrm{130 = 10 + 6x + 8y}\)
• Rearranging: \(\mathrm{6x + 8y + 10 = 130}\)

This matches choice (B) \(\mathrm{6x + 8y + 10 = 130}\)

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students forget to include the base platform in their equation setup.

They focus only on the variable blocks and write: \(\mathrm{6x + 8y = 130}\)

This leads them to select Choice A (\(\mathrm{6x + 8y = 130}\)) because they're only accounting for the riser blocks, not the complete height structure.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret what equals \(\mathrm{130\text{ cm}}\).

They think the blocks alone need to provide \(\mathrm{140\text{ cm}}\) (130 + 10), writing: \(\mathrm{6x + 8y = 140}\)

This may lead them to select Choice C (\(\mathrm{6x + 8y = 140}\)) because they incorrectly added the base platform height to the target instead of recognizing it's part of the total.

The Bottom Line:

This problem tests whether students can correctly identify all components that contribute to a total and TRANSLATE that understanding into proper equation form. The key insight is recognizing that "\(\mathrm{130\text{ cm}}\) tall" means the entire structure, not just the blocks.