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

Question

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

Bytelearn · Accepted Answer

Define Variables: Let's define the variables. Let x represent the number of weeks, and let y represent the account balance after x weeks. Porter's account balance equation: y = 140 + 224x (since he starts with $140 and adds $224 each week). 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. First equation (Porter's account): y = 140 + 224x Second equation (Jasmine's account): y = 231xSet 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 = 231xSolve for x: Solve for x by subtracting 224x from both sides of the equation. 140 + 224x - 224x = 231x - 224x 140 = 7xSubstitute and Calculate: Divide both sides by 7 to solve for x. 140 / 7 = 7x / 7 x = 20Now 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

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