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. Porter started by putting $\$140$ in his account, and he will deposit an additional $\$224$ each week. Jasmine made no initial deposit, but she will add $\$231$ 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, Porter and Jasmine 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. Porter started by putting

\$140

in his account, and he will deposit an additional

\$224

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

\$231

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, Porter and Jasmine will each have an account balance of

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

Define Variables: Let's define the variables. Let $x$ represent the number of weeks, and let $y$ represent the account balance after $x$ weeks. $\newline$ Porter's account balance equation: $y = 140 + 224x$ (since he starts with $\$140$ and adds $\$224$ each week). $\newline$ Jasmine's account balance equation: $y = 231x$ (since she starts with $\$0$ and adds $\$231$ each week).
Set Up Equations: Set up the system of equations based on the information given. $\newline$ First equation (Porter's account): $y = 140 + 224x$ $\newline$ Second equation (Jasmine's account): $y = 231x$
Set Equations Equal: Since both equations equal $y$ , we can set them equal to each other to find the number of weeks ( $x$ ) when their account balances will be the same. $140 + 224x = 231x$
Solve for x: Solve for x by subtracting $224x$ from both sides of the equation. $\newline$ $140 + 224x - 224x = 231x - 224x$ $\newline$ $140 = 7x$
Substitute and Calculate: Divide both sides by $7$ to solve for $x$ . $\frac{140}{7} = \frac{7x}{7}$ $x = 20$
Substitute and Calculate: Divide both sides by $7$ to solve for $x$ . $\frac{140}{7} = \frac{7x}{7}$ $x = 20$ Now that we have the number of weeks ( $x$ ), we can substitute it back into either of the original equations to find the account balance ( $y$ ). Let's use Porter's equation. $y = 140 + 224(20)$
Substitute and Calculate: Divide both sides by $7$ to solve for $x$ .
$\frac{140}{7} = \frac{7x}{7}$
$x = 20$ Now that we have the number of weeks ( $x$ ), we can substitute it back into either of the original equations to find the account balance ( $y$ ). Let's use Porter's equation.
$y = 140 + 224(20)$ Calculate the account balance.
$y = 140 + 4480$
$y = 4620$