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.
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
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 :)
a. The system of equations that would be a good model for this situation is as follows:
For you (let's call you Y):
y = 50 + 10x
For your friend (let's call him F):
y = 20 + 20x
b. Graphing the system of equations:
Y = 50 + 10x
F = 20 + 20x
c. To determine when you and your friend will have the same amount of money saved, we need to find the x-coordinate where the two graphs intersect. This point represents the number of weeks it will take for you and your friend to have the same amount of money saved.
Looking at the graph, it is clear that the two lines intersect at x = 3.5 weeks. Therefore, after 3.5 weeks, you and your friend will have the same amount of money saved.
a. The system of equations that would be a good model for this situation is:
For you:
y = 10x + 50
For your friend:
y = 20x + 20
Where x represents the number of weeks and y represents the amount of money saved.
b. To graph this system of equations, we can plot the points for both equations and connect them with lines.
For y = 10x + 50:
When x = 0, y = 50
When x = 1, y = 60
When x = 2, y = 70
For y = 20x + 20:
When x = 0, y = 20
When x = 1, y = 40
When x = 2, y = 60
Plotting these points, we can draw the lines:
For your equation, the line passes through (0, 50), (1, 60), and (2, 70).
For your friend's equation, the line passes through (0, 20), (1, 40), and (2, 60).
c. From the graph, we can see that the lines intersect at the point (4, 90). This means that after 4 weeks, you and your friend will have the same amount of money saved, $90.
a. To model this situation, we can use a system of equations with x representing the number of weeks and y representing the number of dollars saved.
For you: y = 10x + 50
For your friend: y = 20x + 20
b. To graph this system of equations, we can plot points on a coordinate plane.
For the equation y = 10x + 50:
Let's calculate some points:
When x = 0, y = 10(0) + 50 = 50
When x = 1, y = 10(1) + 50 = 60
When x = 2, y = 10(2) + 50 = 70
For the equation y = 20x + 20:
When x = 0, y = 20(0) + 20 = 20
When x = 1, y = 20(1) + 20 = 40
When x = 2, y = 20(2) + 20 = 60
Now, let's plot these points on a graph.
c. Looking at the graph, we can see that the two lines intersect at the point (3, 80). This means that at week 3, both you and your friend will have the same amount of money saved, which is $80.