Question

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

The relationship between the monthly rental price *r*, in dollars, and the property’s purchase price *p*, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

- r(p) = 2.5p - 870
- r(p) = 5p - 165
- r(p) = 6.5p - 440
- r(p) = 7.5p - 10

## The correct answer is: r(p) = 7.5p - 10

- We have given that the linear function that represents the relationship will be in the linerar form like

r(p) = ap + b,

where *a *and *b *are constants

and *r*(*p*) = monthly rental price( in dollars) of a property

*price = p *thousands of dollars.

- According to the table, (70, 515) and (450, 3,365) are ordered pairs that should satisfy the function, which leads to the system of equations below.
*70a + b = 515*
*450a + b= 3365*

- Subtracting side by side the first equation from the second

450a+b-70a-b=3365-515

380*a *= 2850;

- Solving for
*a *gives

a= 2,850/380= 7.5

- Substituting 7.5 for
*a *in the first equation of the system gives

525 + b = 515;

- Solving for
*b *gives

b = −10.

- Therefore, the linear function that represents the relationship is

r(p) = 7.5p − 10.

Choices A, B, and C are incorrect because the coefficient of *p*, or the rate at which the rental price, in dollars, increases for every thousand-dollar increase of the purchase price is different from what is suggested by these choices.

*70a + b = 515**450a + b= 3365**a*gives*a*in the first equation of the system gives*b*gives### Related Questions to study

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