SOLUTION: 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 representative informs you that t

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Question 251856: 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 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 illustrated the situation.
b) 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 that you used in part a.
c) 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.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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 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 illustrated the situation.
Ans: x + y = 56
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b)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 that you used in part a.
Ans: y = 3x
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c) 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.
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Substitute for "y" and solve for "x":
3x+x = 56
4x = 56
x = 14 (# of plan1 homes)
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Since y = 3x, y = 3*14 = 42 (# of plan2 homes)
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Cheers,
Stan H.