Claire said that StartFraction 10 Over 15 EndFraction of her CDs are country music. Which statement could be true based upon this relationship?

Question

Two-thirds of Claire’s CDs are jazz music.
One-third of Claire’s CDs are country music.
Claire has 10 country CDs and 5 jazz CDs.
Claire has 10 country CDs and 15 jazz CDs.

Answer 1

To analyze the fraction \( \frac{10}{15} \) of Claire's CDs that are country music, we can simplify it to \( \frac{2}{3} \). This means that two-thirds of her CDs are country music.

Now, let's evaluate the statements:

1. Two-thirds of Claire’s CDs are jazz music.

   • This cannot be true, as two-thirds of her CDs are country music, leaving only one-third for other types, including jazz.

2. One-third of Claire’s CDs are country music.

   • This also cannot be true, as we established that two-thirds of her CDs are country music.

3. Claire has 10 country CDs and 5 jazz CDs.

   • If Claire has 10 country CDs, that means her total number of CDs is \( 10 / (2/3) = 15 \). The 5 jazz CDs would then be one-third of her total, which is consistent. This statement could be true.

4. Claire has 10 country CDs and 15 jazz CDs.

   • If Claire has 10 country CDs, her total number of CDs would again be 15, but that would mean she has 15 jazz CDs, making her total 25. This does not fit the ratio established; thus, this statement cannot be true.

Based on the analysis, the only statement that could be true is:

Claire has 10 country CDs and 5 jazz CDs.