Math Word Problem help!?

Question

There are several problems here if you can help me with any of them it is greatly appreciated!!
1) in 1980 the average price of a home in buckeye county was 90 000$. By 1986 the average price of a home was 114 000$. Which of the following represents the price of a home,P, in buckeye country in terms of the year,t? let t=0 correspond to 1980.
The answer is P=4000t +90,000 <-How do i get that answer

2)The intensity ,I, of light received from a source varies inversely as the square of the distance, d, from the source. If the light intensity is 2 foot candles at 11 feet, find the light intensity at 19 feet (round answer to nearest 100th)
The Answer is .67<-How do i get that?

3)find the dimensions of a rectangle whose perimeter is 30 feet and whose area is 56 square feet.
The answer is: 8ft. by 7ft <-how do i get this?

Answer 1

1. 114000-90000 is 24,000 24,000/6 is 4000. This is not real realistic since it is more likely to grow somewhat exponentially.

2. (11/19)^2*2=.67

3. 2x+2y=30 or x+y=15
x*y=56

you can substitute in problem 3 if you wish.

Answer 2

1) It's just a line. Your y-intercept, when t = 0 (defined to be the value in year 1980), is m = 90,000.

Next, you need to find slope. In 6 years, the value increased by:
114000 - 90000 = 24000
So the gain per year was:
24000 / 6 = 4000
therefore b = 4000.

The equation for a line is y = mx + b:
y = 4000t + 90000

2) It says that the intensity varies inversely as the square of the distance.
I = x / (d^2)

We are given that at d = 11 feet, I = 2, so:
2 = x / (11^2)
x = 2 * 121
x = 242 candelas

Use that in the equation again, but with d = 19 feet:
I = 242 / (19^2)
I = 0.67036, or I = 0.67

3) Area is width times height, perimeter is double the width plus double the height.

A = w*h
P = 2w + 2h

Solve perimeter equation for width:
30 = 2w + 2h
2w = 30-2h
w = 15 - h

Plug this into area equation:
56 = w*h
56 = (15 - h)*h
56 = 15h - h^2
h^2 - 15h + 56 = 0

Quadratic equation (show your work!)
Your roots are 7 and 8. Checking your work, you'll find that this is correct (besides, you have the answer already =P).

Answer 3

add then subtract then multiply by 4 then divide by 21