Problem Solving Question

Question

I was set the challenge of answering the question below but after much thought I still can't find an answer. It seems so simple, but not sure of the method needed. The question is:

A mobile app available only on iPhone and Android has 600,000 users who log on an average of 11 times a month. iPhone users log in an average of 7 times a month. Android users log in an average of 13 times a month. What proportion of users have an iPhone?

Any help please.

Answer 1

You can first calculate the total number of iPhone users (x).

$600,000\cdot 11=x\cdot 7+(600,000-x)\cdot 13$

On the LHS it is the total number of the log ins.

The RHS is the sum of the log ins of the iPhone users and the log ins of the Android users.

Then the porportion of the iPhone users is $p^i=\frac{x}{600,000}$

Answer 2

Here's a hint.

Maybe look at the number of logins per month ($6.6$ million).

Call the number of iPhone users $x$. Then the number of logins by iPhone users in a month is $7x$.

Can you take it from here?

Answer 3

We must assume something additional like "total iPhone users' app log ins in a given month / total iPhone app users in a given month = 7", and similarly for Android users. Letting $p$ be the number of iPhone users and $a$ be the number of Android users, we have from the first line:

$p+a=600,000$, and $(7p+13a)/(p+a)=11$.

Solve for $p$ and $a$.