Question

Steve started with $250 and spent $25 per week. Chelsea started with $30 and saved $30 per week. Use x for time and y for savings =. Write and graph equations to represent each situation. When did Steve and Chelsea have the same amount of money?

Answer 1

Steve and Chelsea had the same amount at week 4, $150.00. The equation for Steve is y=250-(25x) and the equation for Chelsea is: y= 30x+30

The graphs are shown above:

To understand how I got the equations:

Steve starts at 250 and keeps wasting $25.00 per week. If he keeps on doing this he’ll lose the original amount, which was $250.00. 25 is our constant rate, so we multiply that by how many weeks he’s been spending and subtract that answer from $250.00.

Chelsea starts of her savings with $30.00 and every week it increases by that much. We have to use 30, our constant rate and multiply that by the amount of weeks she’s been saving and add that to what she started, which is also $30.00

If you have any other questions I’d be glad to answer!

Answer 2

The graph of each situation is attached below

The red line represents y = 250 - 30x

The blue line represents y = 30 + 30x

Steve and Chelsea have the same amount of money after 3.7 weeks

Original amount owned by Steve = $250

Amount spent per week = $30

Let the number of weeks be x

Amount remaining with Steve is calculated as:

y = 250 - 30x..................(1)

Original amount owned by Chelsea = $30

Amount saved per week = $30

The number of weeks = x

Amount owned by Chelsea after x weeks is:

y = 30 + 30x...................(2)

For Steve and Chelsea to have the same amount:

250 - 30x = 30 + 30x

30x + 30x = 250 - 30

60x = 220

x = 220/60

x = 3.7 weeks

Steve and Chelsea have the same amount of money after 3.7 weeks