Sure, let's solve this step-by-step.
Given the equations:
[tex]\[ \frac{x}{5} = \frac{2}{3} \][/tex]
[tex]\[ \frac{5}{y} = \frac{2}{3} \][/tex]
First, solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{x}{5} = \frac{2}{3} \][/tex]
To isolate [tex]\( x \)[/tex], multiply both sides by 5:
[tex]\[ x = 5 \times \frac{2}{3} \][/tex]
[tex]\[ x = \frac{10}{3} \][/tex]
[tex]\[ x = 3.\overline{3} \][/tex]
So, [tex]\( x = 3.333333333333333 \)[/tex].
Next, solve for [tex]\( y \)[/tex]:
[tex]\[ \frac{5}{y} = \frac{2}{3} \][/tex]
To isolate [tex]\( y \)[/tex], take the reciprocal of both sides and then multiply both sides by 5:
[tex]\[ y = 5 \times \frac{3}{2} \][/tex]
[tex]\[ y = \frac{15}{2} \][/tex]
[tex]\[ y = 7.5 \][/tex]
Finally, find the ratio of [tex]\( x \)[/tex] to [tex]\( y \)[/tex]:
[tex]\[ \frac{x}{y} = \frac{3.333333333333333}{7.5} \][/tex]
Calculate the ratio:
[tex]\[ \frac{3.333333333333333}{7.5} = 0.4444444444444444 \][/tex]
Therefore, the ratio of [tex]\( x \)[/tex] to [tex]\( y \)[/tex] is:
[tex]\[ \frac{x}{y} = 0.4444444444444444 \][/tex]
