3.2 Graphing Systems of Equations

Where did you see the solution to the system of equations on the graph?

Tatiana starts with $8 in her piggy bank and saves $2 per week. Julian starts with $0 in his piggy bank and saves $4 per week.

1. Write an equation to model how much money Tatiana has in her piggy bank after x weeks.

2. Write an equation to model how much money Julian has in his piggy bank after x weeks.

Calculate how much John saves each month.

Calculate how much Brenda saves each month.

Both Brenda and John have worked at BuildIt for one year. Answer the following questions by either using the Desmos graph or your equations from Questions 3 and 5.

a. How much money does John have in his savings account after one year?

b. How much more money does John have saved than Brenda after one year?

c. One way to measure the wage gap is to consider how many additional months one person has to work to have the same total earnings, or in this case savings, as another. During which month will Brenda surpass John’s 1-year savings total?

John and Brenda both want to have $25,000 saved, so they can be ready to pay for a down payment on a house.

a. After how many months will John have met his goal?

b. After how many months will Brenda have met her savings goal?

c. How can you use the graph to find those points?

Brenda is considering increasing how much she saves each month, so she can meet her goal sooner.

a. How much would she need to save each month to reach $25,000 at the same time as John? Hint: You can use the Desmos graph from Question 7 to help answer this question.

b. How did you find the answer to part a? Describe your process or show your work.

Which family has the highest savings account balance after 3 weeks? Approximately how much do they have?

After how many weeks do the Green family and the Purple family have the same amount in savings? Justify your response algebraically.