To find the value of [tex]\( x \)[/tex] in the equation [tex]\( \frac{1}{5} x - \frac{2}{3} y = 30 \)[/tex] when [tex]\( y = 15 \)[/tex], follow these steps:
1. Start by substituting [tex]\( y = 15 \)[/tex] into the equation:
[tex]\[
\frac{1}{5} x - \frac{2}{3} \cdot 15 = 30
\][/tex]
2. Calculate [tex]\( \frac{2}{3} \cdot 15 \)[/tex]:
[tex]\[
\frac{2}{3} \cdot 15 = \frac{2 \cdot 15}{3} = \frac{30}{3} = 10
\][/tex]
3. Substitute this value back into the equation:
[tex]\[
\frac{1}{5} x - 10 = 30
\][/tex]
4. Add 10 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{5} x - 10 + 10 = 30 + 10
\][/tex]
[tex]\[
\frac{1}{5} x = 40
\][/tex]
5. To solve for [tex]\( x \)[/tex], multiply both sides of the equation by 5:
[tex]\[
x = 40 \cdot 5
\][/tex]
6. Perform the multiplication:
[tex]\[
x = 200
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 200 \)[/tex]. The correct answer is:
- 200
