SOLUTION: The band is selling bags of cookies as a fundraiser. they will sell chocalate mint cookies for $2.00 a box and oatmeal raisin cookies for $3.00 a box. after 1 day they had sold $1

Question 74958: The band is selling bags of cookies as a fundraiser. they will sell chocalate mint cookies for $2.00 a box and oatmeal raisin cookies for $3.00 a box. after 1 day they had sold $135.00 worth of cookies.
i) define your varibles (what are they and what do they represent?)
ii) write an equation in standard form that represents this situation.
iii) write the equation in slope-intercept form.
iv) make a graph that represnts this situation.
v) list two combinations of cookies types that result in
$135.00 worth of cookies.
vi) what are the x- and y- intercepts, and what do they mean?
vii) how would the equation change if they had sold $180.00 worth of cookies instead?
viii) draw the new line on the same graph as the original.
ix) how does the new graph compare to the original?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The band is selling bags of cookies as a fund-raiser. they will sell chocolate mint cookies for $2.00 a box and oatmeal raisin cookies for $3.00 a box. after 1 day they had sold $135.00 worth of cookies.
:
i) define your variables (what are they and what do they represent?)
Let x = no. of bags of chocolate mints
Let y = no. of bags of oatmeal raisins
:
ii) write an equation in standard form that represents this situation.
2x + 3y = 135
:
iii) write the equation in slope-intercept form.
3y = 135 - 2x
y = (135/3) - (2/3)x
y = 45 - (2/3)x
y = -(2/3)x + 45 is the slope intercept form
:
iv) make a graph that represents this situation.
Plot this graph using the above equation, choose x values that are multiples
of 3, like 6 and 30, and solve for y. table should look like this:
x | y
--------
6 | 41
30 | 25
Plot these coordinates, your graph should look like this:

:
v) list two combinations of cookies types that result in
$135.00 worth of cookies.
Use the values we used to plot the graph, 6 choc, 41 oatm and 30 choc, 25 oatm
:
:
vi) what are the x- and y- intercepts, and what do they mean?
:
The x intercept occurs when y = 0 (no oatm cookies) occurs when (2/3)x = 45
That would be when x = 67.5, hard to sell half a box, however
:
The y intercept occurs when x = 0 (no choc cookies) obviously, that would be
45 bags of oatm cookies
:
:
vii) how would the equation change if they had sold $180.00 worth of cookies instead?
2x + 3y = 180
3y = 180 - 2x
y = 180/3 - (2/3)x
y = 60 - (2/3)x
y = -(2/3)x + 60 is the slope intercept form
Plot this just like we did the other one, substitute for x and solve for y
:
viii) draw the new line on the same graph as the original.

:
ix) how does the new graph compare to the original?
They have the same slope but different x & y intercepts
:
How about this? Did it make sense to you? Any questions?
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