Question

write an equation for the following math sentence. one third times the difference of thirty and a variable is \\(\frac{3}{4}\\). \\(\bigcirc\\) \\(\frac{1}{3}(30 - y)=\frac{3}{4}\\) \\(\bigcirc\\) \\(\frac{1}{3}(y - 30)=\frac{3}{4}\\) \\(\bigcirc\\) \\(\frac{1}{3}(30)-y = \frac{3}{4}\\) \\(\bigcirc\\) \\(\frac{1}{3}y - 30=\frac{3}{4}\\)

Explanation:

Step1: Analyze "the difference of thirty and a variable"

The difference of thirty (30) and a variable (let's say \( y \)) is \( 30 - y \) (since "difference of a and b" is \( a - b \) when \( a > b \) contextually here).

Step2: Analyze "one third times" the difference

"One third times" the difference (\( 30 - y \)) means multiplying \( \frac{1}{3} \) with \( 30 - y \), so that's \( \frac{1}{3}(30 - y) \).

Step3: Analyze "is \( \frac{3}{4} \)"

"Is" translates to the equal sign (\( = \)), so we set the previous expression equal to \( \frac{3}{4} \), giving \( \frac{1}{3}(30 - y) = \frac{3}{4} \).

Answer:

A. \(\boldsymbol{\frac{1}{3}(30 - y) = \frac{3}{4}}\)