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.
I think the answers are x+y=70
x+y(4)=70
but then I also have to solve using the substitution method and I don't get that one!
x + y = 70, IF x = number of of homes with floor plan #1 and y = number of homes with floor plan #2
Then y = 4x
Now use your substitution method.
To solve the problem using the substitution method, let's start with the equations:
a) To represent the situation where there are two floor plans available and a total of 70 houses, we can write the equation as:
x + y = 70
b) To represent the situation where there are 4 times as many homes available with the second floor plan than the first, we can write the equation as:
y = 4x
Now, let's solve these equations using the substitution method:
1. Start with equation b) and solve it for one variable (y in terms of x):
y = 4x
2. Substitute the value of y in equation b) into equation a):
x + (4x) = 70
3. Simplify the equation:
5x = 70
4. Solve for x:
x = 70/5
x = 14
5. Substitute the value of x back into equation b) to solve for y:
y = 4 * 14
y = 56
So, the values of x and y are 14 and 56, respectively. This means that there are 14 houses with floor plan #1 and 56 houses with floor plan #2 in the new housing community under construction.