Suppose you rent apartments in a large apartment complex. Currently there are 90

apartments being rented at a rent of $1300 per month. Evidence shows that for every
increase of $25 per month in rent, there will be 1 additional unit unrented.

(a) U is the number of units rented and R is the amount of rent per month, find a
linear relationship of U in terms of R.

so mainly i relly don't know so good luck

Thanks for stopping by, bob...

If the number of $25 increases is x, then

U = 90-x
R = 1300+25x

So, that means

x = 90-U
x = (R-1300)/25

Equate the two expressions and you have

90-U = (R-1300)/25
U = 90-(R-1300)/25
or
U = 142 - R/25

To find a linear relationship between the number of units rented (U) and the amount of rent per month (R), we need to analyze the given information.

We are told that currently, there are 90 apartments being rented at a rent of $1300 per month. This gives us the first point on the linear relationship: (90, 1300), where U = 90 and R = 1300.

We are also informed that for every increase of $25 per month in rent, there will be 1 additional unit unrented. This means that the rent (R) and the number of rented units (U) have a constant rate of change.

Let's calculate the rate of change by comparing two points. If we increase the rent by $25, one unit will be unrented. So, we can add the rate of change to the initial rent to find the new rent for 89 rented units:

1300 + (89/1) * 25 = 1300 + 2225 = 3525

Therefore, when U = 89, R = 3525. This gives us the second point on the linear relationship: (89, 3525).

Now we have two points: P1(90, 1300) and P2(89, 3525). We can use these points to find the equation of the linear relationship using the slope-intercept form of a linear equation: y = mx + b.

First, we need to find the slope (m):

m = (R₂ - R₁) / (U₂ - U₁)
m = (3525 - 1300) / (89 - 90) = 2225 / (-1) = -2225

Next, we can substitute one of the points (e.g., P1) and the slope into the equation and solve for b:

1300 = -2225 * 90 + b
1300 = -200250 + b
b = 200250 + 1300
b = 201550

Therefore, the linear relationship of U in terms of R is:

U = -2225R + 201550

Thus, to predict the number of units rented (U) based on the rent (R), you can use the equation U = -2225R + 201550.