2. As you are leaving the community, you notice another new community just down
ID: 3103562 • Letter: 2
Question
2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.a) The sales representative here tells you they also have two floor plans available, but they only have 44 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.
b) The representative tells you that floor plan #1 sells for $165,000 and floor plan #2 sells for $210,000. She also mentions that all the available houses combined are worth $7,530,000. Write an equation that illustrates this situation. Use the same variables you used in part a.
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Explanation / Answer
a) let x = floor plan 1 let y = floor plan 2 total number of homes available is 44 x + y = 44 b) 165,000x + 210,000y = 7,530,000 c) solve equation a) for y y = 44 -x substitute into equation b 165,000x+ 210,000(44 - x) = 7,530,000 multiply 165,000x + 9,240,000 - 210,000x = 7,530,000 combine x terms -45,000x + 9,240,000 = 7,530,000 substract 9,240,000 from both sides -45,000x = -1,710,000 divide by -45,000 x = 38 find y using equation a) y = 44 - x y = 44 -(38) y = 6
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