Download 2.3 – Formulas and Problem Solving

2.3 – Formulas and
Problem Solving
Objective: I will be able to solve a
formula for a specified variable.
I will be able to apply formulas to
solve problems.
Formulas
I = PRT
 Interest = principal x rate x time
 A = lw
 Area = length x width
 d = rt
 Distance = rate x time
 C = 2πr
 Circumference = 2 x π x radius
 V = lwh
 Volume = length x width x height

Solve V = lwh for h

To solve V = lwh, isolate h on one side of
the equation.
 V = lwh
V
lwh

lw
lw
V
h
lw
Solving equations for a specific
variable





Step 1: Clear the equation of fractions by multiplying each
side of the equation by the least common denominator.
Step 2: Use the distributive property to remove grouping
symbols such as parentheses.
Step 3: Combine like terms on each side of the equation.
Step 4: Use the addition property of equality to rewrite the
equation as an equivalent equation with terms containing the
specified variable on one side and all other terms on the
other side.
Step 5: Use the distributive property and the multiplication
property of equality to isolate the specified variable.
Solve: 3y – 2x = 7 for y
3 y – 2x = 7
3y – 2x + 2x = 7 + 2x
3y = 7 +2x
2x  7
y
3
Try It! 
Solve 2 y + 5 x = 10 for y
Solve: A = ½ (B + b)h for b
1
A  B  b  h
2
1
2  A  2  B  b  h
2
2A  (B  b ) h
2A  Bh  bh
2A  Bh  bh
2 A  Bh bh

h
h
2 A  Bh
b
h
Try it! 
1
A   B  b h for B
2
Finding the amount in a savings
account
Karen just received an inheritance of
$10,000 and plans to place all the
money in a savings account that pays
5% compounded quarterly to help her
son go to college in 3 years. How
much money will be in the account in
3 years?
1. Understand – Read and re-read the
problem.
r 

A  P 1  
n

nt
A = Amount in the account after t years
P = principal or amount invested
t = time in years
r = annual rate of interest
n = number of times compounded per year.
2. Translate P
= $10,000
 r = 5% = 0.05
 t = 3 years
n = 4
Substitute
r 

A  P 1  
n

nt
0.05 

A  10,000  1 

4 

43
Solve
0.05 

A  10,000  1 

4


43
A  10,000 1.0125 
12
A  10,000 (1.160754518)
A  11,607.55
Interpret

Ask yourself…Is this a reasonable answer?
You try! 
 If
$5,000 is invested in an account
paying 4% compounded monthly,
determine how much money will
be in the account in 2 years.
Finding Cycling Time
 The
fastest average speed by a cyclist
across the continental United States is
15.4mph, by Pete Penseyres. If he
traveled a total distance of about
3107.5 miles at this speed, find his
time cycling. Write the time in days,
hours, and minutes.
1. Understand
 Read
and re-read the problem.
 Appropriate formula: d = rt
d = distance traveled
 r = rate
 t = time

2. Translate
d
= 3107.5 miles
 r = 15.4 mph
 Need
to find time
Substitute
d = rt
3107.5 = 15.4t
t  201.79
You try! 
If a distance of 567 miles at a
speed of 52.5 mph, find the
time.