Question

Currently, Jodi has a collection of 44 CDs and Veronica has a collection of 22 CDs. Jodi is adding 2 CDs per month to her collection; Veronica plans to add 4 CDs per month.

a. Write a system of equations for this situation. Explain your method.
b. Graph the system of equations. Describe your graph.
c. In how many months will they have the same number of CDs? What will be the number of CDs? Explain how you found the answer.
d. At the end of 2 months, who will have more CDs? Explain how you found the answer.

Answer 1

for this you should have 2 equations one for Jodi and one for veronica

for jodi she has a collection of 44 so thats your y-int
and she adds 2 cds per month so your slope is 2
so Jodi's equation is y=2x+44

for veronica its the same method
and you should get y=4x+22

for part b you can graph it by plugging in points, and you should get 2 upward sloping lines that intersect each other

for part c they have the same number of cds when the lines intersect each other so you set them each to each other and solve for x

to find the end of 2 months just plug in 2 for x and see which number is greater

Answer 2

part a)

The equation for Jodi is y = 2x + 44

The equation for Veronica is y = 4x + 22

So the system of equations is

y = 2x+44
y = 4x+22

and they're treated together as one entity so to speak

Answer 3

oh ok

Answer 4

part b)

the line y = 2x + 44 goes through the two points (0,44) and (1,46)

plug in values of x to get corresponding values of y...this gives you points that lie on the line

the line y = 4x+22 goes through (0,22) and (1,26)

Graph each pair of points separately, draw straight lines through them, and make sure the two lines are on the same xy axis

Answer 5

part c)

you can either use the graph to see where the two lines cross or you can do it algebraically

y = 2x + 44

4x + 22 = 2x + 44 ... plug in y = 4x+22

now solve for x

once you get x, use it to find y

Answer 6

part d)

plug in x = 2 into both equations and see which value of y is larger

Answer 7

oh ok \

Answer 8

make more sense? or still stuck somewhere?

Answer 9

nope i am good thanks

Answer 10

ok great