Question

Sam knows that his annual homeowners insurance premium is $0.27 per $100 of value, which usually works out to be $683.10 annually. But Sam is confused by a letter from his insurance company telling him that an increase in the value of his home has led to an increase in his annual homeowners insurance premium. He is now being charged an annual premium of $720.90. Based on the increase in his annual homeowners insurance premium, what was the increase in his home's value? (Note: The cost is still $0.27 per $100, even though the annual premium went up.)

a.
$140
b.
$1,400
c.
$14,000
d.
$140,000

Answer 1

c.

$14,000

Explanation:

Let x be the value of the home

We can use a ratio to solve

.27 insurance

------ = -----------

100 x

.27 683.10

------ = -----------

100 x

Using cross products

.27x = 100 *683.10

.27x=68310

Divide by .27

x = 68310/.27

x = 253000

This is the original value of the home

Now using the new premium

.27 720.90

------ = -----------

100 x

.27x = 720.90*100

.27x = 72090

Dividing by .27

x = 72090/.27

x =267000

The increase is the new value minus the original value

267000-253000

14000

Answer 2

9514 1404 393

Answer:

c. $14,000

Explanation:

The increase in Sam's premium was ...

$720.90 -683.10 = $37.80

The home value increase this corresponds to can be found using the proportion ...

(value increase)/(premium increase) = value/premium

(value increase)/37.80 = 100/0.27 . . . . . . . . . . . . fill in known quantities

value increase = 37.80×100/0.27 = 14,000 . . . . .multiply by 37.80

Sam's home increased in value by $14,000.