To determine the value of \( x \) in the equation \(\frac{1}{5} x - \frac{2}{3} y = 30\) when \( y = 15 \), follow these steps:
1. Substitute \( y \) with 15 in the equation:
[tex]\[
\frac{1}{5} x - \frac{2}{3}(15) = 30
\][/tex]
2. Calculate \(\frac{2}{3}(15)\):
[tex]\[
\frac{2}{3} \times 15 = \frac{2 \times 15}{3} = \frac{30}{3} = 10
\][/tex]
Thus, the equation becomes:
[tex]\[
\frac{1}{5} x - 10 = 30
\][/tex]
3. Isolate \(\frac{1}{5} x\) by adding 10 to both sides:
[tex]\[
\frac{1}{5} x = 30 + 10
\][/tex]
[tex]\[
\frac{1}{5} x = 40
\][/tex]
4. Solve for \( x \) by multiplying both sides by 5:
[tex]\[
x = 40 \times 5
\][/tex]
[tex]\[
x = 200
\][/tex]
So, the value of [tex]\( x \)[/tex] when [tex]\( y = 15 \)[/tex] is [tex]\(\boxed{200}\)[/tex].
