Okay so now I am working on the substitiution portion of this assignment and I understand the first part by not the second can someone help?
Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city.
a) The sales representative informs you that there are two floor plans still available, and that there are a total of 70 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.
b) The sales representative later indicates that there are 4 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. Show all detail calculations.
The answer to A I believe is x+y=70 and the answer to B is x+y(4)=70
Can someone tell me if I am right and where I go from here?
You're on the right track! Let's break it down:
a) From the information given, you have two floor plans: x (floor plan #1) and y (floor plan #2). The total number of houses available is 70. You correctly wrote the equation as x + y = 70.
b) The sales representative informs you that there are 4 times as many homes available with the second floor plan (y) than the first floor plan (x). To represent this using an equation, you can write y = 4x. This equation illustrates that the number of houses with floor plan #2 is four times the number of houses with floor plan #1.
c) Now, let's solve the system of equations using substitution. We have two equations:
1) x + y = 70
2) y = 4x
To use substitution, we'll solve one equation for one variable (preferably the one that's easier to isolate) and substitute it into the other equation.
Let's solve equation 2) for y:
y = 4x
Now, substitute this expression for y in equation 1):
x + (4x) = 70
Simplify the equation:
5x = 70
Divide both sides by 5 to isolate x:
x = 14
Now substitute the value of x back into equation 2) to find y:
y = 4(14)
y = 56
So, there are 14 houses with floor plan #1 (x) and 56 houses with floor plan #2 (y) in this housing community.
It's important to show all the detailed calculations to make it clear how you arrived at your answer.