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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.
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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
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ii) write an equation in standard form that represents this situation.
2x + 3y = 135
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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
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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
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6 | 41
30 | 25
Plot these coordinates, your graph should look like this:
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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
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vi) what are the x- and y- intercepts, and what do they mean?
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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
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The y intercept occurs when x = 0 (no choc cookies) obviously, that would be
45 bags of oatm cookies
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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
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viii) draw the new line on the same graph as the original.
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ix) how does the new graph compare to the original?
They have the same slope but different x & y intercepts
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How about this? Did it make sense to you? Any questions?
