Math for Grownups (11 page)

• An
appraisal fee
is charged when your lender needs to establish the actual value of the home.

• The
title fee
covers the cost of ensuring that the home belongs to the seller, a process called a title search. This fee may also include title insurance, which protects the lender against an error in the title search.

How can you figure out what all of these costs will add up to? Fortunately, the Real Estate Settlement Procedures Act (RESPA) requires that all lenders give the borrower a Good Faith Estimate (GFE) of all the fees associated with the loan. This way, you will have a general idea of how much you’ll need to pay in closing costs.

But as the name suggests, a Good Faith Estimate is just that—an estimate. The actual fee may be slightly lower or higher.

At Home: Will Your New Fridge Fit?

Ah! Home sweet home! Even if you’re not inclined to watch marathons of
This Old House
on PBS, sprucing up your digs can be a rewarding experience.

Except when it isn’t.

Simple projects like painting a room or hanging curtains can become complicated—and expensive—math problems. How much paint do you need? Where should you hang the curtain rods so that the drapes “puddle” just as they do on the cover of
Home Interiors
magazine?

Math probably can’t help you pick out the perfect shade of green for a south-facing room, but it does factor in the economics and geometry of home improvement.

So grab your confidence and a tape measure and get started!

Narcissa is so ready to redecorate her bedroom. Against their better judgment, her parents are letting her use her favorite shade of eyeliner—midnight blue—for the walls, but only on three conditions: She buys the paint, she does the work (and cleans up), and she repaints the room in a more, well,
traditional
shade before she leaves the nest.

Narcissa carefully hides her girlish excitement and responds by shrugging her shoulders and rolling her darkly rimmed eyes. Then she picks off a little of the black polish on the nail of her right index finger.

Her boyfriend Bruno and BFF Absinthe can help transform her ordinary room this Saturday, so Narcissa gets to work figuring out how much paint she needs to buy.

A quick web search reveals that a gallon of paint will cover about 350 square feet. But Narcissa figures she’ll need to apply at least two coats, because the paint color is so dark. (Two years of art classes haven’t gone to waste.) So, she’ll need twice as much paint—just to be on the safe side.

Narcissa cranks up The Cure on her iPod and starts measuring. She’s quick with fractions, and she finds the dimensions of her room and sketches a diagram before the last chord of “Boys Don’t Cry.”

And it’s no wonder: Her room is basically a box—no nooks and crannies, although she’d love to live in the turret of a grand Victorian house.

The ceilings are 8 feet tall. Two walls are 14 feet wide, and the other two walls are 20 feet wide. From listening to dorky Mr. Sneft, her math teacher, she knows that to find the area of each wall, she’ll just multiply the length (or, for our purposes, the height) and the width:

14 • 8
=
112 square feet

20 • 8
=
160 square feet

The mathematical abbreviation for “square feet” is ft
²
. Narcissa knows that two walls are 112 ft
²
and two walls are 160 ft
²
. That means the total square footage of the walls is

112
+
112
+
160
+
160
=
544 ft
²

(Narcissa hasn’t forgotten about the ceiling. Instead of painting it, she’s decided to upholster it with a huge piece of purple velvet. The girl has ambitious plans
and
an amazing sense of style.)

How does she figure out how much paint she needs? She divides the total square footage by 350, which is the number of square feet that 1 gallon of paint is supposed to cover.

544 / 350
=
1.55 gallons

But remember, midnight blue will probably require two coats, so Narcissa multiplies by 2.

1.55 • 2
=
3.1 gallons

No paint store will sell her that exact amount, so Narcissa rounds up and buys 4 gallons of midnight blue paint.

But she
could
do something else. Remember, there are 4 quarts in 1 gallon. Another way to put this: 1 quart is 0.25 gallon. In this situation, she could buy 3 gallons and 1 quart, because 3.25 gallons (3 gallons + 1 quart) is larger than 3.1 gallons (the amount of paint she needs).

Now all Narcissa needs is the velvet.

If you’re looking around your living room right now, envisioning what it would look like in midnight blue, you’ve probably spotted something we didn’t take into consideration in our above calculation: doors and windows. Because Narcissa isn’t going to paint the windows in her room (unless she’s
really
into Goth) and probably not the doors, either, shouldn’t she consider subtracting out the square footage of the windows and doors in order to reach a more exact calculation of how much paint she’ll need? If she needs to be extra careful about her purchase, sure.

Luckily, the experts have figured out two simple rules:

Most doors are about 20 ft
²

Most standard windows are 15 ft
²

Narcissa has 4 windows and 2 doors, so she does these calculations:

So, if we add 40 + 60, we’ll see that the windows and doors take up 100 ft
²
of the room—area that she’s not going to paint. So she can subtract that from the total she found earlier:

544
-
100
=
444 ft
²

And she can divide by 350 again to find out how many gallons it will take to cover 444 square feet:

444 / 350
=
1.27

Then she needs to multiply by 2 (for the two coats of paint):

1.27 • 2
=
2.54

You may have noticed that Narcissa used the formula for the area of a rectangle to find the total square feet in each wall.

A = lw

A
is the area of the wall

l
is the length of the wall

w
is the width of the wall

Then she added the areas of all the walls to find the
surface area
of her walls.

In school, you probably spent some time finding the total surface area of solids, such as prisms and pyramids. In these cases, you found the area of each side and then added them together. But sometimes you want the surface area of only some sides—like the walls of a room, but not the ceiling or floor. In this case, you only need to add the areas of the sides that you’re interested in.

If you think of a room as a three-dimensional figure (specifically, a rectangular prism), it’s easy to see how this would work for all types of 3-dimensional shapes.

No funny-looking glasses required.

Narcissa should be just fine with 2½ gallons of paint (in other words, 2 gallons and 2 quarts). That’s quite a bit less than her original calculation!

When Bruno picks up Narcissa to go to the paint store, he looks at her calculations. “You did this wrong,” he mutters glumly.

Narcissa grabs the paper from his gloved hand and looks again.

“No I didn’t!” she hollers.

“Look,” Bruno says, “I remember that Dear Aunt Sally stuff, and you’ve done the math in the wrong order. You have to
multiply
before you
divide
.”

He grabs the paper from Narcissa’s hand, fishes a stubby pencil from the front pocket of his black jeans, and scribbles down some numbers.

444 ft
²

2 coats of paint

444 • 2
=
888 ft
²

888 / 350
=

He stops and scratches his long goatee with the nub of his pencil. “Huh.”

Narcissa gloats. “See, I did it right,” she says. “888 divided by 350 is 2.54. Hah!”

Why are both of them right? Because it doesn’t matter whether you multiply first or divide first.

In other words, PEMDAS = PEDMAS (Please Excuse Dark Moods And Songs).

Remember what I said about there often being different ways to reach the same answer?

In the morning, it can be awfully tough to crawl out of bed—and when the hardwood floor is freezing, Micah dreads the thought of leaving his cocoon of blankets.

He decides it’s time to put in some fluffy shag carpet, with a pile so deep that he won’t be able to see his toes. Heaven!

But Micah doesn’t trust those guys at Budget Carpet. Sure, their prices can’t be beat, but he’s certain they’re making up the difference by overestimating the amount of carpet customers need. He decides to figure out how much carpet he’ll need, before
they
start measuring.

In short, he needs to know the area of his floor. This would be no problem if his floor were a perfect square—or a rectangle. But it’s not! He has an L-shaped room: the main part, plus an alcove.

Micah takes some measurements and draws a sketch of his room. Then, squinting, he realizes that his L-shaped room is actually 2 rectangles. That gives him an idea for how to solve his problem. All he has to do is find the area of each of these rectangles and then add them together. Violà! He measures the main part of the room. The length is 15 feet, and the width is 33 feet. He calls the area of this part of the room Area 1, or
A
₁
:

A
₁
= 15 • 33

A
₁
= 495 ft
²

Next he measures the alcove, which is a square that measures 25 feet
by 25 feet. He calls the area of this part of the room Area 2, or
A
₂
:

A
₂
= 25 • 25

A
₂
= 625 ft
²

To figure the total amount he needs, or
A
, he adds together
A
₁
and
A
₂
:

A
=
A
₁
+
A
₂

A
= 495 + 625

A
= 1,120 ft
²

So Micah needs 1,120 ft
²
of carpeting. What if he wants to carpet his walk-in closet, too? Then he just needs to find the area of the floor and add that to the 1,120 ft
²
he already knows he needs.

What’s the price tag of that gorgeous shag carpet that Micah wants to install? Budget Carpet has a deal for $10.99 per square yard. So he needs to do a little more math to see whether he can actually afford this luxury. His floor is 1,120 ft
²
. How many square yards is that?

There are 3 feet in a yard, so the calculation is pretty simple. Just divide the number of square feet that you need by 9.

Wait! Why 9? Don’t you divide by 3?

Nope. Remember, you’re working with squared units. There are 3 feet in a yard, so there are 9 square feet in a square yard. (Yep, all you’ve done is squared 3—that is, multiplied itself by itself—to get 9.)

Micah breaks out his trusty calculator and comes up with

1,120 / 9
=
124.44444444…

Because the decimal is less than ½, he should round down, right? Not so fast. When ordering materials, it’s always best to round up; that way you have a little extra, just in case, instead of not enough. So it looks like Micah might want to order 125 square yards of carpet.

That means he’ll pay

$10.99 • 125

$1,373.75

And that doesn’t include the installation fees.

Maybe buying an area rug or a nice pair of wool socks is a better plan.

When Micah was calculating the area of his bedroom, why did he use the little number at the bottom right corner of his variables? Remember how he referred to Area 1 as
A
₁
and to Area 2 as
A
₂
? That little number is called a subscript, and it’s how Micah distinguished between the area of his main room and the area of his alcove. In other words,

A
₁
is the area of the main room.

A
₂
is the area of the square.

A
is the total area of the floor.

But why not use completely different letters? Why not call the area of the main room
m
, the area of the alcove
a
, and the total area
T
?