Answer:
After 13 months both Anna and Moussa will have $150
Explanation:
We can write the money Anna and Moussa has as a linear equation, using slope intercept form:
In this context the slope would represent how much money is being saved/spent, and the y-intercept represents the initial amount, since the y-intercept is the y-value when the x-value is zero. Since the y-value is money, the y-intercept is how much money each of them has after zero months which is just their initial amount.
Anna has an initial amount of $540, and is spending $30 every month, so the slope is negative since the amount Anna has is decreasing by $30 every month.
This means we can represent the amount of money Anna has using the equation:
Moussa has an initial amount of $85, and is saving $5 each money, so the slope is positive since the amount Moussa has is increasing by $5 every month.
This means we can represent the money Moussa has using the equation:
If we want to find when they equal each other, we can simply set both equations equal to each other.
Now let's use some algebraic manipulation to solve, let's start by adding 30x to both sides
Now let's subtract 85 from both sides
Now let's divide both sides by 35 to isolate x
This just gives us how many months it takes for them to be equal to each other, not the amount they'll have. We can find this amount by plugging in this x-value into either equation, since we solved for when they were equal so this x-value outputs the same y-value for both equation.
Let's use the equation we use to represent the amount Moussa has:
simplify
We can double check this by also plugging in 13 into the equation representing Anna's amount to see if they're equal
They're equal so we're sure this solution is correct and the y-value associated with it is 150, which represents the money they'll have when they're equal after 13 months.