Up Your Score (34 page)

Examples:

x
exceeds
y
by 7                    means
x
−
y
= 7 or
y
+ 7 =
x

x
is greater than
y
by 7          means
x
−
y
= 7 or
y
+ 7 =
x

Rule 3:
Percent
(%) usually goes with
of
.

Remember that
percent
means
per hundred
, so a percent problem is really just a problem with fractions. They tell you the numerator and give you the “%” sign, which you translate into meaning “over one hundred.” For example, 25% is really
, which is a fraction.

25% of
y
becomes
of
y
(remember
of
means multiply), so it’s
×
y
or, if you’re using a calculator, .25 ×
y
.

Do the same thing for percentages greater than 100%. For instance, 250% means
, or 2.5.

Rule 4: But wait, there’s
more
. Percent can be made trickier with the word
more
.

If Sue has 25%
more
apples than Bill, then she has
as many
apples as Bill
plus
25% more. So the word
more
can be broken down into “
as many
——
plus
——.”

But we can do better than apples:

Bill has exactly 8 pairs of underwear, all of which
are sexy. Sue has 50% more pairs of underwear
than Bill. 75% of Sue’s total collection of underwear
is sexy.

Who has more sexy underwear? (Don’t get distracted.)

Here’s the answer:

By Rule 4, Sue has
as many
pairs as Bill
plus
50%.

So, Sue has 8 pairs +
of 8.

Sue has 8 + 4 = 12 pairs of underwear.

75% of her 12 total pairs of underwear is sexy.

Using Rule 3, this becomes
of 12.

And finally, using Rule 1, this becomes
× 12 = 9.

Sue has 9 pairs of sexy underwear and Bill has 8, so Sue has more. But they both have about as much fun.

Rule 5: There’s even more.
Percent increase or decrease
means subtract or add.

Jim has $50.00, which he invests wisely; it increases by 10%. How much money does he now have?

Percent means per hundred, so a 10 percent increase means that you add 10% of the original number. 10% of $50 is $5, so $50 + $5 = $55.00. The same holds true for percent decrease.

Rule 6:
Ratio
—okay, so what’s a ratio? A ratio is just a comparison.

If you say
y
>
x
then you’re comparing
y
and
x
and finding out that
y
is larger than
x
. (And, you might ask, who really cares?)
But
y
>
x
is not a ratio. Ratios involve “division comparisons”:

“the ratio of
y
to
x
is 5” means
= 5

Here,
y
is being compared to
x
. Again
y
is bigger—but now we know that
y
is five times bigger. (Wow. Excitement.) This expression could also be written:

“
y
is to
x
as 5 is to 1” or
y
:
x
as 5:1

Okay, well, how
is
5 to 1? 5
is
five times as big as 1 (obviously). So
y
is five times
x
, get it?

It’s probably easiest to think of this as a fraction: