Question

Two friends are renting a property with a monthly rent of $975.00. The total square footage is 1,225 square feet, the first bedroom is 150 square feet, and the second bedroom is 130 square feet. Determine how much the friend with the smaller bedroom will pay for rent if they split the cost based on the square footage of each bedroom. (2 points)

$479.50
$481.35
$495.50
$501.35

Answer 1

(a) $479.50

Explanation:

You want to know how much the friend with the smaller bedroom will pay for rent if they split the $975 cost based on the square footage of each bedroom. The two bedrooms in the 1225 square foot property are 130 and 150 square feet.

Split

Apparently, the cost of the non-bedroom area is to be split evenly. That common area is ...

1225 ft² -(150 +130) ft² = 945 ft²

Then the proportion due from the occupant of the smaller bedroom is ...

(945/2 +130)/1225 = 241/490 ≈ 0.49184

Rent

That fraction of the rent is ...

0.49184 · $975 = $479.54

The nearest answer choice is $479.50.

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Additional comment

If we were to assume the split is based only on bedroom size, then the rent paid for the 130 ft² space would be (13/28)($975) ≈ $452.68. This would be equivalent to splitting the rent for the common area in the same proportion as for the bedrooms.

We note that half the rent is $487.50, a number less than either of the last two answer choices. Those can be rejected for that reason. (The smaller bedroom is expected to pay less than half of the rent.)