This is a 3 part question and it is confusing me quite a bit. Please Help!
a) A real estate agent trying to sell you a home in a new developement tells you that two floor plans are available. use x for floor plan 1 and y for floor plan 2. in total there are 56 homes available. Write and equation of that illustrates thesituation.
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.
I will get you started:
a) x+y=56
b) x=3y or x-3y=0
Sure, let's go through each part step by step:
a) To write an equation that illustrates the situation described in part a, we need to consider the total number of homes available and the number of each floor plan. Let's say the number of homes with floor plan 1 (x) is represented by "x" and the number of homes with floor plan 2 (y) is represented by "y". The total number of homes available is given as 56.
So, the equation can be written as:
x + y = 56
This equation represents the fact that the number of homes with floor plan 1 (x) plus the number of homes with floor plan 2 (y) equals the total number of homes available (56).
b) In part b, it is stated that there are three times as many homes available with the second floor plan as with the first. This means that the number of homes with floor plan 2 (y) is three times the number of homes with floor plan 1 (x).
So, the equation can be written as:
y = 3x
This equation represents the fact that the number of homes with floor plan 2 (y) is equal to three times the number of homes with floor plan 1 (x).
c) Now, we have a system of equations with two unknowns (x and y) based on the equations from part a and part b. To solve the system of equations using substitution, we can substitute the expression for y from part b into the equation from part a.
We can rewrite the equation from part a as:
x + (3x) = 56
Simplifying this equation gives:
4x = 56
To solve for x, we divide both sides of the equation by 4:
x = 14
Now that we have the value of x, we can substitute it back into the equation from part b to find the value of y:
y = 3(14) = 42
Therefore, there are 14 homes available with floor plan 1 (x) and 42 homes available with floor plan 2 (y) in the new development.