To solve the problem where [tex]\( y \)[/tex] is 20% more than [tex]\( x \)[/tex], and we need to find the ratio [tex]\( x : y \)[/tex], follow these steps:
1. Establish the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- Since [tex]\( y \)[/tex] is 20% more than [tex]\( x \)[/tex], [tex]\( y \)[/tex] can be expressed as:
[tex]\[
y = x + 0.2x = 1.2x
\][/tex]
2. Determine the given ratio:
- The ratio of [tex]\( x \)[/tex] is given as 5.
3. Calculate the corresponding ratio for [tex]\( y \)[/tex]:
- [tex]\( y \)[/tex] as a multiple of [tex]\( x \)[/tex] is [tex]\( 1.2 \)[/tex]. Therefore, if [tex]\( x \)[/tex] corresponds to 5 in the ratio, [tex]\( y \)[/tex] can be calculated as:
[tex]\[
y \text{ ratio} = 1.2 \times 5 = 6
\][/tex]
4. Write the final ratio:
- The ratio [tex]\( x : y \)[/tex] is:
[tex]\[
5 : 6
\][/tex]
Thus, the ratio [tex]\( x : y \)[/tex] is [tex]\( 5 : 6 \)[/tex].
