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...

would A. be y=x+56?

The same question was posted way back in July and elaborately answered by Marth

http://www.jiskha.com/display.cgi?id=1247940781

Oh thank you I did not know that thank you, are the answers correct?

a) To write an equation that illustrates the situation, we'll use the variables x and y to represent the number of houses for each floor plan. Since there are two floor plans available, we have:

x + y = 56

This equation represents the total number of houses available in the new housing community.

b) The sales representative tells us that there are 3 times as many homes available with the second floor plan (y) compared to the first floor plan (x). This can be expressed as:

y = 3x

This equation shows the relationship between the number of houses for the second floor plan and the number of houses for the first floor plan.

c) To solve the system of equations using substitution, we can substitute the value of y from the second equation into the first equation:

x + 3x = 56

Simplifying, we get:

4x = 56

Dividing both sides by 4, we find:

x = 14

Substituting this value of x back into the second equation, we can solve for y:

y = 3(14) = 42

Therefore, there are 14 houses available for floor plan #1 and 42 houses available for floor plan #2.

d) To find the intercepts of the equation in part a, let's set x and y to zero separately and solve for the other variable:

When x = 0,
0 + y = 56
y = 56

When y = 0,
x + 0 = 56
x = 56

So the x-intercept is 56 and the y-intercept is 56.

For part b, the equation is y = 3x. Setting x and y to zero separately, we have:

When x = 0,
y = 3(0) = 0

When y = 0,
0 = 3x
x = 0

So the x-intercept is 0 and the y-intercept is 0.

If we solve the system of equations by graphing, the lines will intersect at the point (14, 42), which represents the number of houses for floor plan #1 and floor plan #2, respectively.