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Solving Percentage Problems: Equations, Proportions, Changes, Study notes of Calculus

Ateneo de Davao University (ADDU)Calculus

Step-by-step instructions on how to solve various percentage problems using the percent equation, proportions, percent of increase or decrease, price changes, and simple interest. It includes examples and formulas to help understand the concepts.

Typology: Study notes

2021/2022

Uploaded on 08/05/2022

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SOLVING PERCENT PROBLEMS
Percent Equation
In problems involving the percent equation, two parts of the equation are given, the other part is unknown.
Percent • Base = Amount
To write the equation, identify the given and unknown parts using the guide below:
"of" translates to "multiply"
"is" translates to "="
The base usually follows "of"
The amount usually follows "is"
"what" identifies the unknown
When the percent is given, convert the percent to decimal form.
EXAMPLE 1: 15 is what percent of 120?
To solve the problem, identify the given and unknown parts:
Given: Base = 120 Unknown: Percent = x
Amount = 15
Equation: 120 • x = 15
120 • x 15
120 120
x 0.125 12.5%
=
==
0.125
120 15.000
Percent Proportion
Problems involving the percent equation can also be solved with the proportion:
Percent Amount (is)
100 Base (of)
=
When the percent is given, drop the percent sign and place the percent over 100. Cross multiply to
solve the proportion.
Example 2: 27 is 45% of what number?
Given: Percent = 45% Unknown: Base = x
Amount = 27
Proportion: 45 27
100 x
=
PBCC Page 1 of 4 SLC Lake Worth Math Lab6/7/2005
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Download Solving Percentage Problems: Equations, Proportions, Changes and more Study notes Calculus in PDF only on Docsity!

SOLVING PERCENT PROBLEMS

Percent Equation

In problems involving the percent equation, two parts of the equation are given, the other part is unknown.

P ercent • B ase = A mount

To write the equation, identify the given and unknown parts using the guide below:

"of" translates to "multiply" "is" translates to " = " The base usually follows "of" The amount usually follows "is" "what" identifies the unknown

When the percent is given, convert the percent to decimal form.

EXAMPLE 1 : 15 is what percent of 120?

To solve the problem, identify the given and unknown parts:

Given: Base = 120 Unknown: Percent = x Amount = 15

Equation: 120 • x = 15

120 • x 15 120 120

x 0.125 12.5%

Percent Proportion

Problems involving the percent equation can also be solved with the proportion:

Percent Amount (is) 100 Base (of)

=

When the percent is given, drop the percent sign and place the percent over 100. Cross multiply to solve the proportion.

Example 2: 27 is 45% of what number?

Given: Percent = 45% Unknown: Base = x Amount = 27

Proportion: 45 27 100 x

Next, cross multiply to solve the proportion:

45 27 100 x

45(x) 27(100) 45x 2700 45x 2700 45 45 x 60

Percent of Increase or Decrease

To find the percent of increase or decrease,

  1. Subtract the new amount from the original amount to find the decrease. Subtract the original amount from the new amount to find the increase.
  2. Solve for the percent. The "original amount" is the "base;" the "increase" or "decrease" is the "amount."

Example 3: The amount in a savings account increased from $560 to $672. Find the percent of increase.

  1. Find the increase:

New Amount – Original Amount = Increase

$672 – $560 = $

  1. Solve for the percent:

Given: Base = $560 Unknown: Percent = x Amount = $

Proportion: x^112 100 560

Cross-multiply to solve:

x 112 100 560 560(x) 112(100) 560x 11, 560x 11, 560 560 x 20%

The percent of increase is 20%

At the end of one year the amount in the account is found by adding the interest to the principal:

Principal + Interest = Amount

x + 0.05x = $3,

To find the original investment, solve the equation for x:

x 0.05x 3, 1.05x 3, 1.05x 3, 1.05 1. x 3,

The amount of the original investment was $3,500.