Question

mr. glover wrote the problem, “find 16% of 50” on the whiteboard and asked students to create a proportion or equation to solve the problem. circle the name of anyone who made a true statement.
maxine: i can use the proportion $\frac{x}{50}=\frac{16}{100}$ to solve.
theo: i can find 16% because i can divide 50 by 16.
bryan: i know that 16% of 50 is going to be less than 10 because 10% is 5 and 20% is 10.
elaine: i can change 16% to 1.6 and multiply it by 50.

Explanation:

Step1: Recall percentage - calculation formula

To find \(a\%\) of a number \(n\), we use the formula \(\frac{a}{100}\times n\). Here, \(a = 16\) and \(n=50\), so we need to calculate \(\frac{16}{100}\times50\).

Step2: Simplify the expression

\(\frac{16}{100}\times50=\frac{16\times50}{100}=\frac{800}{100} = 8\).

Let's analyze each student's statement:

• Maxine: She sets up the proportion \(\frac{x}{50}=\frac{16}{100}\), cross - multiplying gives \(100x=16\times50\), then \(x = 8\). Her method is correct.
• Theo: His approach of dividing 50 by 16 is incorrect. To find a percentage of a number, we multiply the number by the fraction representing the percentage, not divide the number by the percentage value.
• Bryan: While his reasoning about comparing with 10% and 20% is correct in terms of magnitude, he doesn't provide a way to solve the problem directly.
• Elaine: Changing 16% to 1.6 and multiplying by 50 is incorrect. 16% is \(\frac{16}{100}=0.16\), not 1.6.

Answer:

Maxine