SOLUTION: Good evening, I am in need of some help solving a word problem and doing an equation set-up. Here is the problem that I am having trouble with. It's 4 parts. The sales repr

Question 95518: Good evening, I am in need of some help solving a word problem and doing an equation set-up. Here is the problem that I am having trouble with. It's 4 parts.
The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.
The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a.
Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.
What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this problem? Where would the lines intersect if you solved the system by graphing?
Thanks so much for any help you can provide.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.
EQUATION: x+y = 56
-----------------------
The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a.
EQUATION: y= 3x
--------------
Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.
Substitute 3x in place of y to get:
x+3x=56
4x = 56
x = 14 (# of homes with floorplan #1)
y=3x=3*14 = 42 (# of home with floorplan #2)
-----------------
What are the intercepts of the equation from part a of this problem?
x + y = 56
x-intercept: let y = 0 then x=56 is the x-intercept
----------
y-intercept: let x= 0 then y = 56 is the y-intercept
-----------------
What are the intercepts from part b of this problem?
y = 3x
x-intercept: let y = 0, then x=0 is the x intercept
y-intercept: let x = 0, then y=0 is the y intercept
--------------------
Where would the lines intersect if you solved the system by graphing?
x+y=56
y=3x
---------
x+3x = 56
4x = 56
x = 14
----------
If x = 14, y=3*14 = 42
------------
The lines intersect at (14,42)
--------------------------------

===============
Cheers,
Stan H.

Thanks so much for any help you can provide.

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