Answer:

EXAMPLE 1

243 people out of 400 state that they LIKE dogs. What percent is this?

Solution

243

400

=

0.6075

=

60.75

100

. This is 60.75%.

Notice that the percent can be found from the equivalent decimal by moving the decimal point two places to the right.

EXAMPLE 2

Write each as a percent:

1

4

0.02

2.35

Solutions

1

4

=

0.25

= 25%

0.02 = 2%

2.35 = 235%

PERCENTS

If we have a part that is some percent of a whole, then

percent

=

part

whole

, or equivalently,

part

⋅

whole

=

percent

.

To do the CALCULATIONS, we write the percent as a decimal.

EXAMPLE 3

The sales tax in a town is 9.4%. How much tax will you pay on a $140 purchase?

Solution

Here, $140 is the whole, and we want to find 9.4% of $140. We start by writing the percent as a decimal by moving the decimal point two places to the left (which is equivalent to dividing by 100). We can then compute: tax = 0.094(140) = $13.16 in tax.

EXAMPLE 4

In the news, you hear “tuition is expected to increase by 7% next year.” If tuition this year was $1200 per quarter, what will it be next year?

Solution

The tuition next year will be the current tuition PLUS an additional 7%, so it will be 107% of this year’s tuition: $1200(1.07) = $1284.

Alternatively, we could have first calculated 7% of $1200: $1200(0.07) = $84.

Notice this is not the expected tuition for next year (we could only wish). Instead, this is the expected increase, so to calculate the expected tuition, we’ll need to ADD this change to the previous year’s tuition: $1200 + $84 = $1284.

TRY IT NOW

A TV originally priced at $799 is on sale for 30% off. There is then a 9.2% sales tax. Find the price after including the discount and sales tax.

EXAMPLE 5

The value of a car dropped from $7400 to $6800 over the last year. What percent decrease is this?

Solution

To compute the percent change, we first need to find the dollar value change: $6800 – $7400 = –$600. Often we will take the absolute value of this amount, which is called the absolute change: |–600| = 600.

Since we are computing the decrease relative to the starting value, we compute this percent out of $7400:

\displaystyle\frac{600}{7400}=0.081=

7400

600

=0.081= 8.1% decrease. This is called a relative change.

ABSOLUTE AND RELATIVE CHANGE

Given two quantities,

Absolute change =\displaystyle|\text{ending quantity}-\text{starting quantity}|∣ending quantity−starting quantity∣

Relative change: \displaystyle\frac{\text{absolute change}}{\text{starting quantity}}

starting quantity

absolute change

Absolute change has the same units as the original quantity.

Relative change gives a percent change.

The starting quantity is called the base of the percent change.

I HOPE THIS HELPFULL FOR YOU