Questions: Solve the problem for x. Record the answer using a whole number. 1/20 : 1/40 :: x: 25

Transcript text: Solve the problem for $x$. Record the answer using a whole number. $\qquad$ \[ \frac{1}{20}: \frac{1}{40}:: x: 25 \]

Solution

Solution Steps

Step 1: Understand the proportion

The given proportion is: \[ \frac{1}{20} : \frac{1}{40} :: x : 25 \] This can be interpreted as: \[ \frac{\frac{1}{20}}{\frac{1}{40}} = \frac{x}{25} \]

Step 2: Simplify the left side of the proportion

Simplify $\frac{\frac{1}{20}}{\frac{1}{40}}$: \[ \frac{\frac{1}{20}}{\frac{1}{40}} = \frac{1}{20} \times \frac{40}{1} = 2 \] So, the proportion becomes: \[ 2 = \frac{x}{25} \]

Step 3: Solve for $ x $

Multiply both sides of the equation by 25 to isolate $ x $: \[ 2 \times 25 = x \] \[ x = 50 \]