Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Yesterday, two friends went into a bank to open savings accounts. Anita started by putting $\$826$ in her account, and she will deposit an additional $\$45$ each week. Felipe made no initial deposit, but he will add $\$104$ 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, Anita and Felipe will each have an account balance of $\$\_\_\_\_\_$ .

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Grade 8

Solve a system of equations using substitution: word problems

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

\newline

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

\$826

in her account, and she will deposit an additional

\$45

each week. Felipe made no initial deposit, but he will add

\$104

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, Anita and Felipe will each have an account balance of

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

Define Variables: Let's define the variables. $\newline$ Let $x$ represent the number of weeks. $\newline$ Let $A$ represent Anita's account balance. $\newline$ Let $F$ represent Felipe's account balance.
Write Equations: Write the equations based on the given information. $\newline$ Anita's account balance starts at $\$826$ and increases by $\$45$ each week. So, $A = 826 + 45x$ . $\newline$ Felipe's account balance starts at $\$0$ and increases by $\$104$ each week. So, $F = 104x$ .
Set Equal: Set the two expressions equal to each other to find when the account balances will be the same. $826 + 45x = 104x$
Solve for x: Solve for x using the substitution method. $\newline$ Subtract $45x$ from both sides to get all the x terms on one side. $\newline$ $826 + 45x - 45x = 104x - 45x$ $\newline$ $826 = 59x$
Calculate Balances: Divide both sides by $59$ to solve for $x$ . $\newline$ $826 \div 59 = x$ $\newline$ $x \approx 14$
Verify Balances: Calculate the account balance for Anita and Felipe after $x$ weeks. $\newline$ Since $x$ is approximately $14$ , we'll use that to find the account balance. $\newline$ $A = 826 + 45(14)$ $\newline$ $A = 826 + 630$ $\newline$ $A = 1456$
Check Solution: Verify that Felipe's account balance is the same after $14$ weeks. $\newline$ $F = 104(14)$ $\newline$ $F = 1456$
Check Solution: Verify that Felipe's account balance is the same after $14$ weeks. $\newline$ $F = 104(14)$ $\newline$ $F = 1456$ Check if the solution makes sense and if there are no mathematical errors. $\newline$ Both Anita and Felipe have the same account balance of $\$1456$ after $14$ weeks, which matches the solution we found. There are no mathematical errors.