Interest and tax payments involve finding percents. You can use the percent proportion to solve these kinds of problems. However, it is usually easier to write the percent proportion as an equation.
The equation P RB is called the percent equation.
In this equation, R is the rate. The rate is the decimal form of the percent.
The percent equation is easier to use when the rate and base
are known. However, the percent equation can be used to solve any percent
problem.
Example
1. Find 4% of $160.
Alternative
Solutions :
P = RB Use the
percent equation.
= 0.04(160) Replace
R with 0.04 and B with 160.
= 6.4 0.04
× 160 = 6.4
So, 4%
of $160 is $6.40.
2. 12 is 60% of what number?
Alternative
Solutions :
P = RB Use
the percent equation.
12 = 0.6B Replace P with 12 and R with 0.6.
Divide each
side by 0.6.
20 = B 12
÷ 0.6 = 20
So, 12 is
60% of 20.
Many real-world problems can be solved by using the percent
equation.
Example
Tax Link
3. The Federal Insurance Contributions Act (FICA) requires employersto
deduct 6.2% of your income for social security taxes. Suppose your weekly pay
is $140. What amount would be deducted from your pay for social security taxes?
Alternative
Solutions :
To
find the amount deducted, find 6.2% of 140.
P = RB Use the percent equation.
= 0.062(140) Replace R
with 0.062 and B with 140.
= 8.68 0.062
× 140 = 8.68
So, $8.68
would be deducted from your pay.
Percents are also used in simple interest problems. Simple interest is the
amount paid or earned for the use of money. If you have a savings account, you
earn interest. If you borrow money through a loan or with a credit card, you
pay interest.
The formula I = prt is used to solve problems
involving interest.
• I represents
the interest,
• p represents
the amount of money invested or borrowed, which is called the principal,
• r represents
the annual interest rate, and
• t represents
the time in years.
Example
Banking Link
4. Rodney Turner is opening a savings account that earns 4% annual interest.
He wants to earn at least $50 in interest after 2 years. How much money should
he save in order to earn $50 in interest?
Alternative
Solutions :
I = prt
50 = p(0.04)(2) Replace
I with 50, r with 0.04, and t with
2.
50 =
0.08p 0.04 × 2 = 0.08
Divide
each side by 0.08.
625 = p 50
÷ 0.08 = 625
Rodney should invest at least $625 to earn $50 in interest.
Mixture problems involve combining two or more parts into a whole. The
parts that are combined usually have a different price or a different percent
of something.
Example
Sales Link
5. Crystal sold tickets to the Drama Club’s spring play. Adult tickets cost
$8.00, and student tickets cost $5.00. Crystal sold 35 more student tickets
than adult tickets. She collected a total of $1475. How many of each type of
ticket did she sell?
Alternative
Solutions :
Explore
Let a be the number of adult tickets that Crystal sold.
Since there were 35 more student tickets sold than
adult tickets, a +
35 is the number of student tickets sold.
Plan Make a chart of the information.
Solve 8a + 5(a + 35) = 1475 Original equation
8a + 5a + 175 = 1475 Distributive Property
13a + 175 = 1475 8a + 5a = 13a
13a + 175 – 175 = 1475 – 175 Subtract 175 from each side.
13a = 1300 Simplify.
Divide
each side by 13.
a = 100 Simplify.
Crystal sold 100 adult tickets and 100 + 35 or 135 student tickets.
Examine
If 100 adult tickets
were sold, the total amount
of money collected for them would be 100 × 8 or $800.
If 135 student tickets were sold, the total amount of money
collected for them would be 135 × 5 or $675.
The total sales would be $800 + $675 or $1475.
Mixture problems occur often in chemistry.
Example
Finance Link
6. Kelsey is doing a chemistry experiment that calls for a 30% solution of
copper sulfate. She has 40 milliliters of a 25% solution. How many milliliters
of a 60% solution should she add to make the required 30% solution?
Alternative
Solutions :
Let x represent the amount of 60% solution
to be added. Since she starts with 40 milliliters of solution, the final
solution will have 40 + x
milliliters.
0.25(40)
+ 0.60x = 0.30(40 + x) Original
equation
10 +
0.6x = 12 + 0.3x Distributive
Property
10 +
0.6x – 0.3x = 12 + 0.3x – 0.3x
Subtract 0.3x from each side.
10 +
0.3x = 12 Simplify.
10 +
0.3x – 10 =
12 – 10 Subtract
10 from each side.
0.3x = 2 Simplify.
Divide
each side by 0.3.
x ≈ 6.7 2
÷ 0.3 = 6.666666667
Kelsey
should add about 6.7 milliliters of the 60% solution.
Sumber
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