Question

the art museum is giving away tickets to the greco exhibit. today, the museum expects to give away 150 percent of the 800 tickets that it gave away yesterday. martin is trying to figure out how many tickets the museum will give away today. his work is shown below.

\\(\frac{\text{part}}{\text{whole}} = \frac{150}{100}\\)

\\(100 \times 8 = 800\\)

\\(150 \div 8 = 18.75\\)

what mistake did martin make?

• martin should have multiplied 150 by 8.
• martin should have divided 100 by 8.
• martin should have added 150 and 800.
• martin should have multiplied 150 and 800.

Explanation:

Identify the given proportion

The problem uses a percent proportion:

$$ \frac{\text{part}}{\text{whole}} = \frac{150}{100} $$

Here, the whole is \(800\).

Analyze the scale factor

To find the equivalent fraction with a denominator of \(800\):

$$ \frac{\text{part}}{800} = \frac{150}{100} $$

Since \(100 \times 8 = 800\), the scale factor is \(8\).

Identify Martin's error

To keep the ratio equivalent, the numerator must also be multiplied by the same scale factor:

$$ \text{part} = 150 \times 8 $$

Martin divided \(150\) by \(8\) instead of multiplying.

Answer:

• Martin should have multiplied 150 by 8. (Correct answer)
• Martin should have divided 100 by 8.
• Martin should have added 150 and 800.
• Martin should have multiplied 150 and 800.