Question

josiah’s work:
\\(\frac{10}{20} = \frac{x}{1,500}\\)
\\(\frac{10 \times 30}{20 \times 30} = \frac{x}{1,500}\\)
\\(300 = x\\)
\\(\circ\\) he should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
\\(\circ\\) he did not multiply the numerator and denominator by the correct number to equal 1,500.
\\(\circ\\) his answer will be one - half of what he got because he did not divide 10 by 2 when setting up the proportion.
\\(\circ\\) he can only solve the proportion by multiplying the numerator and denominator by a common multiple.
\\(\circ\\) he should have multiplied the numerator and denominator by 75, not 30, because \\(20 \times 75 = 1,500\\).

Explanation:

Step1: Check denominator scaling factor

To make denominator 20 equal to 1500, calculate $\frac{1500}{20}=75$.

Step2: Analyze Josiah's error

Josiah used 30 instead of 75. Verify $20 \times 75 = 1500$, not $20 \times 30$.

Step3: Evaluate all options

• Option 1: Irrelevant to proportion solving.
• Option 2: Vague, does not specify the correct number.
• Option 3: Incorrect, no need to divide 10 by 2.
• Option 4: False, cross-multiplication is also valid.
• Option 5: Correct, identifies the right scaling number.

Answer:

He did not multiply the numerator and denominator by the correct number to equal 1,500.
He should have multiplied the numerator and denominator by 75, not 30, because $20 \times 75 = 1,500$.