# The value of the building lot for the given conditions.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.11, Problem 44E
To determine

## To find: The value of the building lot for the given conditions.

Expert Solution

The value of the given building lot is $51,200 . ### Explanation of Solution Given: The value of a building lot on Galiano island is jointly proportional to its area and the quantity of water produced by a well on the property. Dimension of the building lot is 200ft×300ft . Quantity of water produced by the well is 10gal/min . Value of the building lot is$ 48,000

Calculation:

The equation of the given variation is,

C=k(Aq) (1)

Here,

C is the value of the building lot, A is the building lot, q is the quantity of water produced by the well, and k is constant of proportionality.

To find the value of a building lot whose area is 400ft×400ft and quantity of water produced by well is 4gal/min , first calculate the value of constant of proportionality.

Substitute 200×300 for A , 10 for q and 48000 for C in equation (1)

C=k(Aq)48000=k((200×300)10)48000=k(600000)48000600000=k

Simplify above equation,

k=0.08 (2)

Thus, the value of constant of proportionality is 0.08

Now, use the value of constant of proportionality to calculate the value of a building lot whose area is 400ft×400ft and quantity of water produced by well is 4gal/min .

Substitute 400×400 for A , 4 for q and 0.08 for k from equation (2) in equation (1).

C=k(Aq)C=0.08((400×400)4)C=51200

Thus, the cost of building lot is \$51,200 .

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