Question

mary and aaron each opened a savings account on the same day. mary started by putting $40 in her account, and she will deposit an additional $1 each week. aaron made an initial deposit of $15, and he will add $6 more each week. eventually, mary and aaron will each have the same amount saved. what is that amount? write a system of equations, graph them, and type the solution.

Explanation:

Step1: Define the equations

Let $x$ be the number of weeks and $y$ be the total amount of money saved.
For Mary, the initial deposit is $40$ and she adds $1$ per week, so the equation is $y = 40+x$.
For Aaron, the initial deposit is $15$ and he adds $6$ per week, so the equation is $y=15 + 6x$.

Step2: Set the equations equal

Since we want to find when they have the same amount saved, we set $40+x=15 + 6x$.
Subtract $x$ from both sides: $40=15 + 5x$.
Subtract $15$ from both sides: $25=5x$.
Divide both sides by $5$: $x = 5$.

Step3: Find the total amount

Substitute $x = 5$ into Mary's equation $y=40+x$.
$y=40 + 5=45$.

Answer:

$45$