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Question 135667: Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. (a) The sales rep. 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. (b) The sales rep. later indicates that there are 3 times as many homes available with the 2nd floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a. (c) Use the equations form part a and b as a system of equations, and solve via substitution.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (a) The sales rep. 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
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(b) The sales rep. later indicates that there are 3 times as many homes available with the 2nd floor plan than the first. Write an equation that illustrates this situation.
EQUATION:
x = (1/3)y
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Use the same variables you used in part a.
(c) Use the equations from part a and b as a system of equations, and solve via substitution.
EQUATION: (1/3)y+y = 56
(4/3)y = 56
(1/3)y = 14
y = 42 (# of #2 floor plan houses)
x = (1/3)42 = 14 (# of #1 floor plan houses)
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Cheers,
Stan H.
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