Question

At the beginning of the summer, John has $150 in his bank account. He is starting a part-time summer job and wants to deposit $32 each week. Assuming that John does not make any withdrawals.

Question 1: Write an expression that represents John’s account balance after w weeks.

Question 2: If John’s account balance is $374, how many weeks has he worked?

Question 3: John’s best friend, Marco, works with him over the summer. Marco has an account balance of $185 and deposits the same amount as John each week. Write an expression for Marco’s account balance after w weeks.

Question 4: Marco claims that both he and John will have the same account balance sometime during summer. Is his claim correct? Justify using your work.

Answer 1

Step-by-step explanation:

Division 1 - The expression is w = 32x + 150

Division 2 - The expression is 374 = 32x + 150

374 - 150 = 224

224/32 = 7

John worked for 7 weeks to acquire the amount he needed, which, in this case, was $374.

Division 3 - The expression is w = 32x + 185

Division 4 - Make the two expressions equal each other...

32x + 150 = 32x + 185

32x = 32x -35

32x - 32x = 0

0 = -35

Thus, Marco, nor John will have the same account balance, at any point during the summertime.

Answer 2

Part 1:

Expression: w = 32x + 150

Part 2:

Expression: 374 = 32x + 150

374 - 150 = 224

224/32 = 7

John has worked for 7 weeks to accumulate a total of 374 USD.

Part 3:

Expression: w = 32x + 185

Part 4:

Make the two expressions equal each other:

32x + 150 = 32x + 185

Move 150 to the other side.

32x = 32x -35

32x - 32x = 0

0 = -35

Therefore, at no point will Marco or John have the same account balance at sometime during the summer.