Chapter MPS, Problem 3.4MPS

(a)

To determine

To Find: Equation that represents the given situation

Answer to Problem 3.4MPS

  $\text{⇒}x+\left(2x-16\right)=95\left(\text{equation i}\right)$

Explanation of Solution

Given:

  $\begin{array}{l}\text{sum of two number}=95\\ \text{one number is }16\text{ less than twice the other}\end{array}$

Formula Used:

  $\text{first number}+\text{second number}=\text{sum of two number}$

Calculation:

  $\begin{array}{l}\text{→}\text{Let one number be }x\\ \text{→}\text{other number}=2x-16\\ \text{⇒}\text{sum of both number}=95\\ \text{⇒}x+\left(2x-16\right)=95\left(\text{equation i}\right)\end{array}$

Conclusion:

Thus the equation for the given situation is $x+\left(2x-16\right)=95$

(b)

To determine

To Find: Numbers

Answer to Problem 3.4MPS

  $\begin{array}{l}\text{→}\text{one number }=37\\ \text{→}\text{other number}=58\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{sum of two number}=95\\ \text{one number is }16\text{ less than twice the other}\end{array}$

Formula Used:

  $\text{first number}+\text{second number}=\text{sum of two number}$

Calculation:

  $\begin{array}{l}\text{→}\text{Let one number be }x\\ \text{→}\text{other number}=2x-16\\ \text{⇒}\text{sum of both number}=95\\ \text{⇒}x+\left(2x-16\right)=95\left(\text{equation i}\right)\\ \text{⇒}x+2x-16=95\\ \text{⇒}3x-16=95\\ \text{⇒}3x-16+16=95+16\left(\text{adding both side by 16}\right)\\ \text{⇒}3x=111\\ \text{⇒}\frac{3x}{3}=\frac{111}{3}\left(\text{divide both side by 3}\right)\\ \text{⇒}x=37\\ \text{other number}=2\left(37\right)-16=58\\ \text{→}\text{one number }=37\\ \text{→}\text{other number}=58\end{array}$

Conclusion:

Thus the numbers are $37,58$