(I answered a couple of them but am not confident on my answers, so can you please tell me if my answers are not correct to the ones I answered and for the ones I haven not answered that is because I do not know how to do them. PLEASE HELP!!! This assignment is already late).
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. x+y=56
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. x+y(3)=56
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?
a. is correct
b. is not correct You have the right idea. y = 3x. Now substitute 3x in for y in the equation and solve it.
I am not very confident with algebra and am failing my class. Can you please help with parts c and d?
X + y = 56
y = 3x
Substituting that into the first equation...
x + 3x = 56
combining...
4x = 56
Divide both sides by 4 to find the value for x.
Once you have the value for x, use the second equation of y = 3x to find the value for y.
I'm so sorry that I'm asking so many questions but like I said I do not understand all of this. How do you solve for y in those steps? Please give details so I can better understand it. The answers you gave me, were they just for part c or d too? I think just c right?
a) Your answer is correct. The equation that represents the situation is indeed x + y = 56, where x represents the number of houses with floor plan #1 and y represents the number of houses with floor plan #2.
b) Your answer is incorrect. The equation that represents the situation is x + 3y = 56, where x represents the number of houses with floor plan #1 and y represents the number of houses with floor plan #2. The sales representative stated that there are 3 times as many homes available with the second floor plan than the first, so the coefficient of y should be 3, not y(3).
c) To solve this system of equations using substitution, you can follow these steps:
Step 1: Start with the equation x + y = 56 (equation from part a).
Step 2: Solve this equation for one variable in terms of the other. Let's solve for x in terms of y:
x = 56 - y
Step 3: Substitute this expression for x into the second equation from part b: x + 3y = 56
(56 - y) + 3y = 56
Step 4: Simplify and solve for y:
56 - y + 3y = 56
2y = 0
y = 0/2
y = 0
Step 5: Substitute the value of y back into the equation x + y = 56 to find x:
x + 0 = 56
x = 56
Therefore, there are 56 houses with floor plan #1 and 0 houses with floor plan #2.
d) The intercepts of the equation x + y = 56 can be found by setting one variable to zero and solving for the other:
- x-intercept: Set y = 0, and solve for x:
x + 0 = 56
x = 56
- y-intercept: Set x = 0, and solve for y:
0 + y = 56
y = 56
So the x-intercept is (56, 0) and the y-intercept is (0, 56).
For the equation x + 3y = 56, we can follow the same steps:
- x-intercept: Set y = 0, and solve for x:
x + 3(0) = 56
x = 56
- y-intercept: Set x = 0, and solve for y:
0 + 3y = 56
y = 56/3
y = 18.67 (approximately)
So the x-intercept is (56, 0) and the y-intercept is approximately (0, 18.67).
If you graph the two equations, the lines would intersect at the point (56, 0) which represents the number of houses with floor plan #1 and no houses with floor plan #2.