word problem

Question

Two house are for sale on the same street. The sec house  has 1,000square feet less than twice  the square foot  of the first house. Together  the houses have 4,400 square feet.what is the square footage  of the first  house?

Answer 1

Hi Mary-

This problem requires us to set up two independent equations to solve for two unknowns.  The two unknowns are the square footage of each house, and we have enough information to set up the two independent equations.

Let X = House #1 square footage and Y = House #2 square footage.

From the problem statement:

Equation 1: Y = 2*X - 1000 (the 2nd house, Y, has 1000 sq. ft. less than twice the square footage of the 1st house, X)   

Equation 2: X + Y = 4400 (the total square footage of both houses equals 4400)

Now plug the "value" for Y from the first equation into the second equation:

X + 2*X - 1000 = 4400

Now solve this equation to determine the value of X:

3*X - 1000 = 4400   (combine X terms)

3*X = 5400   (add 1000 to both sides)

X = 5400/3   (divide both sides by 3 to result in unit X)

X = 1800 sq. ft.

And from the second equation, Y = 4400 - 1800 = 2600 sq. ft.

Check by plugging both numbers into the first equation: 2600 = 2*1800 - 1000 = 3600 - 1000 ...check

Answer 2

First we set up the problem:

 

There are two houses. 

 

House 1 has the square feet of X

 

House 2 has the square of house 1 (or X) times 2 and less a thousand, which we can state as: 2X - 1000

 

Both of these together add up to a total square footage of 4400.

 

Put all the items with X values on the left side of the equation, and the total on the right, like this:

 

X + (2X-1000) = 4400

 

now, solve for X.

 

First, add like terms:

 

3X - 1000 = 4400

 

Simplify by adding 1000 to each side:

 

3X = 5400

 

Divide each side by 3:

 

X = 1800

 

Check your work by putting the value into the original equation:

1800 + [(2 X1800) - 1000  = ?

 

1800 + 3600 -1000 = ?

 

The sum is 4400, which is the total square footage of both houses.

 

Therefore, the answer would be:

 

The square footage for the first house would be 1800 square feet.

 

Answer 3

Hi Mary, let x represent the square feet of the first house. Then the second house has 2x - 1000 square feet. Together they have 4400 square feet.

 

Equation:

 

x + (2x - 1000) = 4400

 

Remove the parentheses and combine terms:

 

3x - 1000 = 4400

 

Add 1000 to both sides:

 

3x = 5400

 

Divide both sides by 3:

 

x = 1800

 

Answer:

 

The first house has 1800 square feet.

 

The second house has 2x - 1000, or 3600 - 1000, or 2600 square feet.

 

Questions?