You and your friend are saving for college. You have $50 and are added $10 each week to your savings. Your friend has $20 and he is adding $20 each week to his savings.

Question

a. what system of equations would be a good model for this situation? Let x be number of weeks and y be the number of dollars saved.
b. Graph your system of equations
c. use the graph to determine when you and your friend will have the same amount of money saved. Explain your answer

Answer 1

a.
As the problem hinted,
Let x = number of weeks
Let y = dollars saved
For the first equation: you have initially $50, and $10 is added each week. Therefore, at the end of x weeks, the total amount of money you'll have is,
y = 50 + 10x

For the second equation: same analysis as the first, thus,
y = 20 + 20x

b.
Graphs cannot be shown here, so go to wolframalpha . com , and type the two equations we got above, say,
" plot y = 50 + 10x and y = 20 + 20x "

c.
Note that you should see from the graph, two lines intersecting at one point.
Looking at the graph, get the point of intersection of the two lines. And get the y value (for this is the dollars saved as we have represented).

Hope this helps :)