Analyzing Student Work

A video game that usually costs [tex]\$30.65[/tex] is marked down by [tex]60\%[/tex]. Kelvin determined that the new price of the game would be [tex]\$18.39[/tex]. Look at Kelvin's work and find his error.

[tex](\[tex]$30.65)(0.60) = \$[/tex]18.39[/tex]



Answer :

Sure, let's analyze Kelvin's work step-by-step to identify and correct his error.

### Initial Information
- Original price of the video game: \[tex]$30.65 - Markdown percentage: 60% ### Kelvin's Calculation Kelvin calculated: \[ (\$[/tex] 30.65) \times 0.60 = \[tex]$ 18.39 \] Here, Kelvin found that 60% of the original price is \$[/tex]18.39, which is correct. However, he misunderstood this value. Let's clarify what this value represents and then find the correct new price.

### Correct Approach

1. Calculate the markdown amount:
- Markdown amount = [tex]\( \text{Original Price} \times \text{Markdown Percentage} \)[/tex]
[tex]\[ \text{Markdown amount} = 30.65 \times 0.60 = \$ 18.39 \][/tex]

2. Determine the new price after the markdown:
- New price = Original Price - Markdown Amount
[tex]\[ \text{New price} = 30.65 - 18.39 = \$ 12.26 \][/tex]

### Conclusion

- Markdown amount: [tex]\( \$ 18.39 \)[/tex]
- New price after markdown: [tex]\( \$ 12.26 \)[/tex]

Kelvin's error was in interpreting the value of \[tex]$18.39 as the new price, whereas it actually represents the markdown amount. The correct new price of the game after a 60% markdown is \$[/tex]12.26.