Question 723161
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There is no mention of the amount of paint required to do either the ceiling or the walls in the second room, so let *[tex \LARGE a_2] be the number of gallons of ceiling paint that costs *[tex \LARGE x] dollars per gallon and *[tex \LARGE b_2] be the number of gallons of wall paint that costs *[tex \LARGE y] dollars per gallon.  Let *[tex \LARGE C_2] be the total cost of paint for the second room.


The equation that models the first room is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 4y\ =\ 120]


The equation that models the second room is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a_2x\ +\ b_2y\ =\ C_2]


Knowing the cost relationship between the two types of paint allows us to write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x\ -\ 3]


Then by substitution:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 4(x\ -\ 3)\ =\ 120]


From which you can determine the cost of the ceiling paint.  Using the cost of the ceiling paint, that is to say *[tex \LARGE x], you can then subtract 3 to determine the cost of the wall paint, that is: *[tex \LARGE y].


Once you know the costs you can plug those numbers into:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a_2x\ +\ b_2y\ =\ C_2]


to develop a formula for any size room where the same types of paint are used.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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