I'm struggling with the equations for the following problem:
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.
The answer that I got was 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.
The answer to this one, that I got, is:
x+3y=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.
This is where I am stuck. If I did any of the equations wrong, can you please correct me so that I can get the right answer.
Thanks
your first equation is correct,
your second equation should be
y = 3x
your equation translated into English would say,
" the sum of #1 plan houses plus 3 times the #2 plan houses is a total of 56"
now sub in y = 3x into the first equation
For part a), the equation you wrote as x+y=56 is correct. You used the variables x and y to represent the number of houses for floor plan #1 and floor plan #2 respectively, and since there are a total of 56 houses available, the equation x+y=56 represents this situation accurately.
For part b), you need to write an equation to represent the fact that there are 3 times as many homes available with the second floor plan as the first. Let's use the same variables, x and y, but now we know that the number of homes with the second floor plan, y, is three times the number of homes with the first floor plan, x. So the equation for this situation is x + 3y = 56.
Now, for part c) you are asked to use the equations from parts a) and b) as a system of equations. To determine the number of each type of floor plan available, you can use substitution.
Here are the steps to solve the problem:
1. Start with the equation x + y = 56 from part a).
2. Solve this equation for x in terms of y: x = 56 - y.
3. Substitute the expression for x into the equation from part b): 56 - y + 3y = 56.
4. Simplify the equation: 56 + 2y = 56.
5. Subtract 56 from both sides of the equation: 2y = 0.
6. Divide both sides of the equation by 2: y = 0.
7. Substitute back into the expression for x: x = 56 - 0 = 56.
Therefore, the solution to the system of equations is x = 56 and y = 0. This means there are 56 houses available with floor plan #1 and 0 houses available with floor plan #2.
Let me know if you have any further questions or need additional assistance!