Chapter 11.1, Problem 57AYU

To determine

To determine: The number of commercial and non-commercial orbital launches in 2017 , where there was a total of 469 commercial and non-commercial orbital launches worldwide and the number of non-commercial orbitals was 31 more than half the number of commercial and noncommercial in 2017 .

Answer to Problem 57AYU

Solution:

In 2017 , there are 292 commercial orbital launches and 177 non-commercial orbital launches.

Explanation of Solution

Given information:

In 2017 , there were a total of 469 commercial and noncommercial orbital launches worldwide and the number of non-commercial orbitals was 31 more than half the number of commercial and non-commercial.

Let $x$ be the number of commercial orbital launches and $y$ be the number of non-commercialorbital launches.

A total of 469 commercial and non-commercial orbital launches worldwide.

Therefore, $x+y=469$

The number of non-commercial orbitals were 31 more than half the number of commercial and non-commercial.

Therefore, $y=\frac{x}{2}+31$

Substituting the value of $y$ from the equation $x+y=469$$\Rightarrow x+\frac{x}{2}+31=469$

  $\Rightarrow \frac{3x}{2}=438$

  $\Rightarrow x=\frac{438\times 2}{3}$

  $\Rightarrow x=146\times 2$

  $\Rightarrow x=292$

Substituting the value $x=292$ in the equation $y=\frac{x}{2}+31$

  $\Rightarrow y=\frac{292}{2}+31$

  $\Rightarrow y=146+31$

  $\Rightarrow y=177$

Therefore, there are 292 commercial orbital launches and 177 non-commercial orbital launches.