Questions: Solve the problem for x. Record the answer using one decimal place. 2/5: 1/2:: x: 4

Solution Steps

The given proportion is \(\frac{2}{5} : \frac{1}{2} :: x : 4\). This means \(\frac{2}{5}\) is to \(\frac{1}{2}\) as \(x\) is to \(4\).

The proportion can be written as: \[ \frac{\frac{2}{5}}{\frac{1}{2}} = \frac{x}{4} \]

Simplify \(\frac{\frac{2}{5}}{\frac{1}{2}}\) by multiplying by the reciprocal: \[ \frac{2}{5} \times \frac{2}{1} = \frac{4}{5} \] So, the equation becomes: \[ \frac{4}{5} = \frac{x}{4} \]

Multiply both sides of the equation by \(4\) to isolate \(x\): \[ x = \frac{4}{5} \times 4 = \frac{16}{5} = 3.2 \]

The value of \(x\) is \(3.2\) (rounded to one decimal place).

Final Answer