Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. 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? In _____ weeks, Anita and Felipe will each have an account balance of $_____.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  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?   In _____ weeks, Anita and Felipe will each have an account balance of $_____.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables. Let x represent the number of weeks. Let A represent Anita's account balance. Let F represent Felipe's account balance.Write Equations: Write the equations based on the given information. Anita's account balance starts at $826 and increases by $45 each week. So, A = 826 + 45x. 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 = 104xSolve for x: Solve for x using the substitution method. Subtract 45x from both sides to get all the x terms on one side. 826 + 45x - 45x = 104x - 45x 826 = 59xCalculate Balances: Divide both sides by 59 to solve for x. 826 ÷ 59 = x x ≈ 14Verify Balances: Calculate the account balance for Anita and Felipe after x weeks. Since x is approximately 14, we'll use that to find the account balance. A = 826 + 45(14) A = 826 + 630 A = 1456Check Solution: Verify that Felipe's account balance is the same after 14 weeks. F = 104(14) F = 1456Check if the solution makes sense and if there are no mathematical errors. 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.

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