1. Suppose you are in the market for a new home and are interested in a new hous
ID: 3103561 • Letter: 1
Question
1. 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 52 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 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.
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.
d) 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?
Explanation / Answer
a) x = floor plan 1 y = floor plan 2 total number of houses left is 52 x + y = 52 b) y = 3x c) substitute equation b) into equation a) to get x + (3x) = 52 4x = 52 x = 13 so there are 13 houses with floor plan 1 and y = 3x = 3(13) = 39 so there are 39 houses with floor plan 2 d) for part a x + y =52 rewrite as y = -x + 52 so the y intercept is 52 and the x intercept is 52 for part b) y = 3x so the y intercept is 0 and the x intercept is 0 the lines intersect at x = 13, and y = 39
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