Chapter 11.1, Problem 57AYU

Orbital Launches In $2017$ there was a total of $469$ commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was 31 more than half the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches in $2017$.

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 non-commercial 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.

Explanation:

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