Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Yesterday, two friends went into a bank to open savings accounts. Regan started by putting $\$7$ in her account, and she will deposit an additional $\$363$ each week. Devon made no initial deposit, but she will add $\$370$ more each week. In a few weeks, the friends will have the same account balance. How many weeks will that take? What is that account balance? $\newline$ In $\_\_\_$ weeks, Regan and Devon will each have an account balance of $\$\_\_\_\_\_\_$ .

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Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Yesterday, two friends went into a bank to open savings accounts. Regan started by putting

\$7

in her account, and she will deposit an additional

\$363

each week. Devon made no initial deposit, but she will add

\$370

more each week. In a few weeks, the friends will have the same account balance. How many weeks will that take? What is that account balance?

\newline

\_\_\_

weeks, Regan and Devon will each have an account balance of

\$\_\_\_\_\_\_

Define Variables: Let's define the variables. Let $x$ be the number of weeks, and $y$ be the account balance after $x$ weeks. $\newline$ Regan's account balance equation: $y = 7 + 363x$ $\newline$ Devon's account balance equation: $y = 370x$
Set Equations Equal: Since we are looking for the point where both Regan and Devon have the same account balance, we can set their equations equal to each other to find the number of weeks $x$ . $7 + 363x = 370x$
Solve for x: Solve for x by subtracting $363x$ from both sides of the equation. $\newline$ $7 + 363x - 363x = 370x - 363x$ $\newline$ $7 = 7x$
Find Value of x: Divide both sides by $7$ to find the value of $x$ . $\newline$ $\frac{7}{7} = \frac{7x}{7}$ $\newline$ $x = 1$
Substitute $x$ : Now that we have the number of weeks, we can substitute $x$ back into either Regan's or Devon's account balance equation to find the account balance ( $y$ ). $\newline$ Using Regan's equation: $y = 7 + 363(1)$
Calculate Regan's Balance: Calculate the account balance for Regan after $1$ week. $\newline$ $y = 7 + 363$ $\newline$ $y = 370$
Calculate Devon's Balance: To confirm our solution, we can also substitute $x$ into Devon's account balance equation. $\newline$ Using Devon's equation: $y = 370(1)$
Confirm Solution: Calculate the account balance for Devon after $1$ week. $\newline$ $y = 370$
Confirm Solution: Calculate the account balance for Devon after $1$ week. $\newline$ $y = 370$ Since both calculations for $y$ resulted in the same value, our solution is consistent and correct. $\newline$ In $1$ week, Regan and Devon will each have an account balance of $\$370$ .