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 56 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 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. Describe the steps you used to solve the problem.
d)What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this problem? Where would the lines intersect if you solved the system by graphing?
Can someone please help me? I am weak at word problems at the same time weak at graphing and inequalities, If someone could give me a couple tips or formula how to solve these problems I would appreciate it thank you so much...
Sure, I'd be happy to help you with these word problems and equations.
a) To write an equation that represents the situation, let's use x to represent floor plan #1 and y to represent floor plan #2. Since there are two floor plans still available and a total of 56 houses, we can write the equation as:
x + y = 56
b) The sales representative says there are three times as many homes available with the second floor plan than the first. To represent this situation, we can write the equation as:
y = 3x
c) Now we have a system of equations with two unknowns (x and y). We can solve this system using the substitution method.
Step 1: Start with the equation from part b, which is y = 3x.
Step 2: Substitute this expression for y into the equation from part a, which is x + y = 56.
So, we have:
x + (3x) = 56
Simplifying this equation, we get:
4x = 56
Dividing both sides by 4, we find:
x = 14
Step 3: Substitute the value of x back into the equation from part b to solve for y.
y = 3(14)
y = 42
Therefore, there are 14 houses with floor plan #1 and 42 houses with floor plan #2.
d) To find the intercepts of the equation from part a, let's set one of the variables to zero at a time and solve for the other variable. When x = 0, y = 56. So the y-intercept is (0, 56). When y = 0, x = 56. So the x-intercept is (56, 0).
For the equation from part b, if we set x = 0, y = 0 because y = 3x. Therefore, there are no intercepts for this equation.
If you were to graph these equations, the lines would intersect at the solution of the system, which we found to be (14, 42).