Answered

The average number of weekly social media posts varies jointly with the poster's yearly income (in thousands) and inversely with their age in years.

If a 60-year-old person with an income of [tex]$100,000 posts an average of 300 times in a week, what is the value of $[/tex]k[tex]$?

A. $[/tex]k=300[tex]$
B. $[/tex]k=180[tex]$
C. $[/tex]k=225[tex]$
D. $[/tex]k=100$



Answer :

To solve this problem, let's break it down step-by-step.

We know that the average number of weekly social media posts ([tex]\( P \)[/tex]) varies jointly with the poster's yearly income ([tex]\( I \)[/tex]) in thousands and inversely with their age ([tex]\( A \)[/tex]) in years. This can be expressed mathematically as:

[tex]\[ P = k \times \frac{I}{A} \][/tex]

where:
- [tex]\( P \)[/tex] is the number of posts,
- [tex]\( I \)[/tex] is the yearly income in thousands,
- [tex]\( A \)[/tex] is the age,
- [tex]\( k \)[/tex] is the proportionality constant we need to find.

Given:
- [tex]\( P = 300 \)[/tex] (the average number of weekly posts),
- [tex]\( A = 60 \)[/tex] years,
- [tex]\( I = 100 \)[/tex] (since the income is \$100,000 and we consider it in thousands, so [tex]\( 100,000/1000 = 100 \)[/tex]).

We substitute these values into the equation to solve for [tex]\( k \)[/tex]:

[tex]\[ 300 = k \times \frac{100}{60} \][/tex]

Simplify the fraction [tex]\(\frac{100}{60}\)[/tex]:

[tex]\[ \frac{100}{60} = \frac{10}{6} = \frac{5}{3} \][/tex]

So, the equation becomes:

[tex]\[ 300 = k \times \frac{5}{3} \][/tex]

To isolate [tex]\( k \)[/tex], multiply both sides of the equation by [tex]\(\frac{3}{5}\)[/tex]:

[tex]\[ 300 \times \frac{3}{5} = k \][/tex]

[tex]\[ k = 180 \][/tex]

Thus, the value of [tex]\( k \)[/tex] is 180. The correct answer is:

[tex]\[ k = 180 \][/tex]