Here is a question, but I am having a problem finding the right systems of equation. Are the ones I have written correct?
Question: The mortgage department of the company is selling two model homes that are located on the same block. The square footage, as well as the type of model, determines the cost of these homes.
e) The second home has 1000 square feet less than twice the square feet of the first home. Write an equation that illustrates this situation using x and y to denote home #1 and home #2, respectively.
My first answer
2y=x-1000
f) Together, both homes have 4,400 square feet. Write an equation that illustrates this situation using the same variables you used in part e.
My second answer
2x+2y=4400
The second home has 1000 square feet less than twice the square feet of the first home.
e) y = 2x - 1000
Together, both homes have 4,400 square feet. (Why did you use 2x and 2y?)
f) x + y = 4400
I hope this helps.
3e
To check if your equations are correct, let's analyze each part separately:
e) The equation that represents the situation where the second home has 1000 square feet less than twice the square feet of the first home can be written as:
2x - 1000 = y
In this equation, x represents the square footage of the first home, and y represents the square footage of the second home. Your equation, 2y = x-1000, is incorrect because you reversed the variables x and y.
f) The equation that represents the situation where both homes have a combined square footage of 4,400 can be written as:
x + y = 4400
In this equation, x and y represent the square footage of the first and second homes, respectively. Your equation, 2x + 2y = 4400, is incorrect because you mistakenly multiplied both x and y by 2.
To summarize, the correct equations are:
e) 2x - 1000 = y
f) x + y = 4400
Remember to carefully analyze the given information and translate it into mathematical expressions to solve word problems.