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This situation could be solved using algebra or guess, test, and revise.
Let us ask the family to calculate the price for 1,200 sq. ft.
The price for builder 1= 24,000 + 45.5(1,200)
= 24,000 + 54,600
= 78,600 dollars
The price for builder 2 = 15,000 + 51.5(1,200)
= 15,000 + 61,800
= 76,000 dollars
What if they want to buy a bigger house with a lot of 2,500 sq. ft?
The price for builder 1= 24,000 + 45.5(2,500)
= 24,000 + 113,750
= 137,750 dollars
The price for builder 2 = 15,000 + 51.5(2,500)
= 15,000 + 128,750
= 143,750 dollars
Obviously, for the smaller area, builder 2 is cheaper. For the bigger area, builder 1 is cheaper.
So, it is getting more complicated!!! How can the family decide?
Writing an equation for both builders, we can get the area ( x ) where the two builders would have the same price.
Price for builder 1 = price for builder 2
24,000 + 45.5 (x) = 15,000 + 51.5 (x)
24,000 - 15,000 = 51.5 x - 45.5 x
9,000 = 6 x
x = 1500
So, for an area of 1,500 sq. ft. the price for both builders will be the same.
When the area is more than 1,500 sq. ft., the price of builder 2 will be more than builder 1.
When the area is less than 1,500 sq. ft., the price of builder 1 will be more than builder 2.
Now, it is the family's decision to choose the area they need and the price accordingly.
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