To compare the ratios given by Alyana, let's analyze the ratio [tex]\(3:5\)[/tex]. This ratio tells us that for every 3 pairs of shorts, Alyana has 5 pairs of jeans.
We need to determine which of the following options are equivalent to Alyana's ratio.
1. [tex]\(3:8\)[/tex]
- This ratio means 3 pairs of shorts for every 8 pairs of jeans. This is not asking the same proportion as [tex]\(3:5\)[/tex]. Therefore, this ratio is not equivalent.
2. [tex]\(\frac{3}{5}\)[/tex]
- Writing the ratio as a fraction, [tex]\(3:5\)[/tex] can be expressed as [tex]\(\frac{3}{5}\)[/tex]. This accurately represents the ratio of shorts to jeans, maintaining the same relationship as 3 shorts to 5 jeans. Therefore, this is an equivalent ratio.
3. [tex]\(5:3\)[/tex]
- This reverses the ratio, representing 5 pairs of shorts for every 3 pairs of jeans. While mathematically connected, it does not directly represent [tex]\(3:5\)[/tex], as it talks about a higher number of shorts compared to jeans. This can be seen as an inverse of the given ratio, but it is not the same in terms of who has more or less. Therefore, this ratio is not exactly equivalent to [tex]\(3:5\)[/tex], although it is the inverse relationship.
4. [tex]\(\frac{8}{3}\)[/tex]
- This fraction represents a different proportional relationship—8 pairs of shorts for every 3 pairs of jeans—which does not align with the initial given ratio of [tex]\(3:5\)[/tex]. This is not equivalent.
So, among the choices given, the only ratio that is equivalent to Alyana's [tex]\(3:5\)[/tex] is [tex]\(\frac{3}{5}\)[/tex].
