Bannen – Elem. Alg.
Section 2.5
Name:
Section 2.5: Using Formulas to Solve Problems
In many applications, the equations are already known. Your job is to use the right equation
in the right way:
• pick out the right equation from a list
• plug in the variables that you know (make sure the units are compatible)
• solve for the variable that you don’t (don’t forget to give units with your answer!)
Practice
1. What is the approximate radius of a circle that has a circumference of 22 centimeters
(cm)?
2. A farmer has 800 meters (m) of fencing to enclose a rectangular field. If the width of
the field is 175 m, find the length of the field.
3. The area of a triangle is 120 m2 . If the height is 24 m, find the length of the base.
V ; 8) l = P −2w ; 9) 20 min; 10) $2.84; 11) $31.49; 12) $14,195
Answers: 1) 3.5 cm; 2) 225 m; 3) 10 m; 4) 3 ft2 ; 5) 2 yd; 6) 1.3 in; 7) h = lw
2
Bannen – Elem. Alg.
Section 2.5
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4. A trapezoid has bases of length 5 feet (ft) and 7 ft and a height of 6 inches. What is
its area?
5. A dump truck has a rectangular box that is 3 yards (yd) wide by 5 yd long. What
must be the height of the box if it needs to contain a volume of 30 cubic yards?
6. If a can has a radius of 3.0 inches (in.), what must its height be if it is to hold a volume
of 36 in.3 ?
7. Solve the formula V = lwh for h. (Hint: this is just like problem 5, but you will keep
V , l, and w as letters instead of replacing them with numbers.)
8. Solve the formula P = 2l + 2w for l. (Hint: this is like problem 2.)
Bannen – Elem. Alg.
Section 2.5
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9. If a runner averages 250 meters per minute, how long will it take him to complete a 5
km run?
10. At baseball and football stadiums, the food vendors often price their items so that they
come out even with tax. How much would a vendor need to sell soda for to make the
price with tax come out to $3.00? Assume that tax is 5.5%. (Note: always convert
percentages to decimals in these money problems.)
11. If I bought a shirt at a 10% discount and the original price was $34.99, what was the
discounted price?
12. Carla bought a car for $12,999 and financed it at 4.5% interest, compounded annually.
Then she lost her job and couldn’t make any car payments. How much did she owe
after 2 years?
Topic
Geometry
Perimeter of a rectangle
Circumference of a circle
Area of a circle
Area of a triangle
Area of a trapezoid
Area of a rectangle
Volume of a box
Volume of a sphere
Volume of a cylinder
Surface area of a Box
Surface area of a sphere
Surface area of a cylinder
Chemistry
Density
Equation
Variables
P = 2l + 2w
C = 2πr
A = πr2
A = 21 bh
A = 21 h(b + B)
A = lw
V = lwh
V = 34 πr3
V = πr2 h
S = 2hw + 2lw + 2lh
S = 4πr2
S = 2πr2 + 2πrh
perimeter (P ),length (l), width (w),
circumference (C), radius (r), π ≈ 3.14,
area (A),
base (b), height (h),
big base (B),
m
V
density (d), mass (m),
volume (V )
Dilution
c1 V1 = c2 V2
concentration (c1 , c2 ),
volume (V1 , V2 )
Gas Law
P 1 V1
T1
pressure (P1 , P2 )
volume (V1 , V2 )
temperature (T1 , T2 )
Physics
Motion (constant speed)
d=
=
P2 V2
T2
d = rt
Motion (with acceleration)
d = ri t + 12 at2
rf2 = ri2 + 2ad
Electrical current
V = IR
P = IV
volume (V )
Surface Area (S)
distance (d), rate or speed (r),
time (t),
initial speed (ri ), acceleration (a)
final speed (rf )
voltage (V ), current (I),
resistance (R),
power (P )
Money
Tax
T = S(1 + t)
Discount
T = S(1 − d)
Simple interest
A = P rt
Compound interest
A = P (1 + r)n
Mortgage
P = L[c(1 + c)m ]/[(1 + c)m − 1] loan amount (L),
monthly interest rate (c),
number of months (m),
monthly payment (P )
total (T ), subtotal (S),
tax rate (t),
discount rate (d)
principal (P ), interest rate (r),
time (t), ending amount (A)
number of years (n)