Question

Which proportions are equivalent to$\frac{x}{12}=\frac{3}{4}?$

$(a.)\frac{x}{3}=\frac{12}{4}$ $(b.)\frac{x}{4}=\frac{12}{3}$ $(c.)\frac{12}{x}=\frac{4}{3}$ $(d.)\frac{x+12}{12}=\frac{7}{4}$

Short answer

The given proportion is equivalent to,

$\frac{x+3}{3}=\frac{7}{4}$

Step-by-step solution

Step 1. Given information.

The given proportion is,

$\frac{x}{3}=\frac{3}{4}$

Step 2. Concept used.

For the proportion$\frac{a}{b}=\frac{c}{d}$,

it is equivalent to,$\frac{a+b}{b}=\frac{c+d}{d}$

Step 3. Apply this concept on given proportion.

It is given that,$\frac{x}{3}=\frac{3}{4}$

So, $\frac{x+3}{3}=\frac{3+4}{4}=\frac{7}{4}$

Therefore, the given proportion is equivalent to,

$\frac{x+3}{3}=\frac{3+4}{4}=\frac{7}{4}$