Certainly! To start with, the information given is that Molly has $45, and this amount is three times as much as her brother has. Let us represent Molly’s brother’s amount of money with the variable 'a.'
Now, since Molly has three times as much money as her brother does, we can express this relationship with the following equation:
\[ 45 = 3 \times a \]
This equation shows that if you multiply Molly’s brother's money (a) by 3, you will get the amount that Molly has, which is $45.
We are interested in finding out how much money Molly's brother has. To do this, we need to solve for 'a.' We can do this by dividing both sides of the equation by 3 to isolate 'a.' Here's how it's done:
\[ a = \frac{45}{3} \]
When you divide 45 by 3, you get:
\[ a = 15 \]
Therefore, Molly’s brother has $15. This completes the solution to the problem. The equation to represent the situation is:
\[ 45 = 3 \times a \]
And upon solving this equation, we find that 'a,' the amount of money Molly’s brother has, is $15.