Chapter 7.4, Problem 76HP

To determine

To find the number

Answer to Problem 76HP

5

Explanation of Solution

Given:

Marge takes a number and subtracts 4, multiplies by 4, takes the square root and takes the reciprocal to get $\frac{1}{2}$ .

Let the number be a.

Marge subtracts 4 from the number.

  $\Rightarrow a-4$

Multiplies 4 to the number.

  $\Rightarrow 4(a-4)$

Takes the square root of the number

  $\Rightarrow \sqrt{4(a-4)}$

Takes reciprocal as it gives $\frac{1}{2}$

  $\Rightarrow \frac{1}{\sqrt{4(a-4)}}=\frac{1}{2}$

Therefore, the formula to find the number is $\frac{1}{\sqrt{4(a-4)}}=\frac{1}{2}$

Simplify the expression to find the number.

Cross multiply the expression,

  $1\cdot 2=1\cdot \sqrt{4(a-4)}$

Simplify the expression,

  $2=\sqrt{4(a-4)}$

Square on both sides.

  $2^2={(\sqrt{4(a-4)})}^2$

Simplifying,

  $\begin{array}{l}\Rightarrow 4=4(a-4)\\ \Rightarrow 4=4a-16\\ \Rightarrow 4+16=4a\\ \Rightarrow 20=4a\\ \Rightarrow a=5\end{array}$

Conclusion:

Therefore, the number is $a=5$ .