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. 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? In _____ weeks, Regan and Devon 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. 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?   In _____ weeks, Regan and Devon will each have an account balance of $_____.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables. Let x be the number of weeks, and y be the account balance after x weeks. Regan's account balance equation: y = 7 + 363x Devon's account balance equation: y = 370xSet 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 = 370xSolve for x: Solve for x by subtracting 363x from both sides of the equation. 7 + 363x - 363x = 370x - 363x 7 = 7xFind Value of x: Divide both sides by 7 to find the value of x. 7 / 7 = 7x / 7 x = 1Substitute 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). Using Regan's equation: y = 7 + 363(1)Calculate Regan's Balance: Calculate the account balance for Regan after 1 week. y = 7 + 363 y = 370Calculate Devon's Balance: To confirm our solution, we can also substitute x into Devon's account balance equation. Using Devon's equation: y = 370(1)Confirm Solution: Calculate the account balance for Devon after 1 week. y = 370Since both calculations for y resulted in the same value, our solution is consistent and correct. In 1 week, Regan and Devon will each have an account balance of $370.

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