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What is 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]?

A. 4
B. 8
C. 80
D. 200

Sagot :

GinnyAnswer
To solve for 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. Substitute [tex]\( y = 15 \)[/tex] into the equation:

[tex]\[ \frac{1}{5}x - \frac{2}{3}(15) = 30 \][/tex]

2. Simplify the term involving [tex]\( y \)[/tex]:

[tex]\[ \frac{2}{3} \times 15 = \frac{2 \times 15}{3} = \frac{30}{3} = 10 \][/tex]

So the equation becomes:

[tex]\[ \frac{1}{5}x - 10 = 30 \][/tex]

3. Isolate the term involving [tex]\( x \)[/tex] by adding 10 to both sides of the equation:

[tex]\[ \frac{1}{5}x - 10 + 10 = 30 + 10 \][/tex]

This simplifies to:

[tex]\[ \frac{1}{5}x = 40 \][/tex]

4. Solve for [tex]\( x \)[/tex] by multiplying both sides of the equation by 5:

[tex]\[ x = 40 \times 5 \][/tex]

Therefore:

[tex]\[ x = 200 \][/tex]

So, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{200} \)[/tex].
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