Question

Kevin has $500 in his savings account and he deposits $25 each week. Janet has $250 in her savings account and she deposits $50 each week.

(a) Write a system of equations that represents the scenario

(b) Solve the system to determine after how many weeks Kevin and Janet will have the same amount of savings. What will that amount be?

Answer 1

(a) Let x be the number of weeks and let y be the total amount in their savings accounts. Then, the system of equations that represents the scenario is:

Kevin: y = 25x + 500

Janet: y = 50x + 250

(b) To determine after how many weeks Kevin and Janet will have the same amount of savings, we need to solve the system of equations by setting them equal to each other:

25x + 500 = 50x + 250

Subtracting 25x and 250 from both sides, we get:

250 = 25x

Dividing both sides by 25, we get:

x = 10

Therefore, Kevin and Janet will have the same amount of savings after 10 weeks. To find out what that amount is, we can substitute x = 10 into either equation:

y = 25x + 500

y = 25(10) + 500

y = 750

So after 10 weeks, both Kevin and Janet will have $750 in their savings accounts.

Step-by-step explanation: explained it in the answer