Practice:
Practice: Direct, Inverse, & Joint Variation
Determine the variation then solve the problem.
1. The numbers r and s vary directly and the constant of variation is 3/5.
a) Find the equation:
b) Find r if s = 45
c) Find s if r =33.
2. The amount of heat (H) produced in human body by burning of proteins is directly
proportional to the amount of proteins (A) burnt. If burning of 1 gram of proteins
produces 32 calories of heat, how much proteins should be burnt to produce 52
calories?
a) Write an equation in terms of H and A:
b) Solve the problem
3. The numbers x and y are directly proportional and x = 9 when y = 3.
a) Write the equation:
b) Find x when y = 8
c) Find y when x = 42.
4. A family spends 120 dollars per month for vegetables when the cost of vegetables is 5
dollars per kg. How much must the family spend per month, if the cost of vegetables
goes up to 5.75 dollars per kg?
5. The numbers p and q are directly proportional and p = 7.5 when q = 15. Find p
when q = 38; and find q when p = 13.
6. The weight E of a man on earth's surface is directly proportional to his weight M on
mars. The constant of proportionality is 3, if a man weights 126 kg on earth, how
much will he weigh on mars?
7. At the rate of 28 lines per page, a book has 300 pages. If the book has to contain only
280 pages, how many lines should a page contain?
8. If y varies inversely as x; and x = 6 when y = −3, find y when x = −9.
9. The number 'r ' varies inversely as 's ' and the constant of variation is 20. Find s when
r = 5; and find r when s = −2.
10. It is known that current (A) in an electric circuit is inversely proportional to the
resistance (R) in the circuit. When the resistance is 3 ohms, the current is 2 amperes.
Find the resistance if the current is 5 amperes; and find the current when the R is 4.
11. In an army camp food is inversely related to the number of people at the camp. For
instance there is food for 8 weeks for 1200 people. After 3 weeks, 300 more soldiers
joined the camp. For how many more weeks will the food last?
12. In chemistry, Boyle’s Law says that if temperature is kept constant, the volume of a
gas varies inversely to the pressure. If a certain gas has a volume of 100mL when the
pressure is 150 kPa, write the general inverse variation equation for Boyle’s Law and
find…
a) Equation for this particular gas
b) Volume when the gas has a pressure of 75kPa.
13. F varies jointly as G and H. If G = 2 and H = 3, then F = 35. Find the formula.
14. R varies directly as the square of s. If R = 75, then s = 5. Find the formula.
15. A varies directly as the cube of B. If B = 2, then A = 40. Find the formula.
16. Hookes’s Law for an elastic spring states that the distance a spring stretches varies
directly as the force applied. If a force of 15 pounds stretches a certain spring 8
inches, how much will a force of 30 pounds stretch the spring?
a) Write the equation
b) Solve the problem
17. y varies inversely as the square of x. If x = 5, then y = 3. Write the formula.
18. C varies directly with x and inversely with the square root of w. If x = 4, w = 36,
and C = 10:
a) Write the formula
b) Find the value of C when x = 3 and w = 25
19. T varies jointly with x and the cube of z. If x = 2, z = 3, and T =6:
a) Write the formula
b) Find the value of T when x = 18 and z = 2
20. Natural gas provides 35.8% of U.S. energy. The volume of a gas varies inversely as
the pressure and directly as the temperature. (Temperature must be measured in
degrees Kelvin K, a unit used in physics.) If a certain gas occupies a volume of 2 liters
and 300K and a pressure of 18 newtons per square centimeter, find the volume at
340K and pressure of 24 newton per square centimeter.
a) Write the equation
b) Solve the problem
21. The body-mass index or BMI, is used by physicians to assess a person’s BMI. The
BMI varies directly as an individual’s weight in pounds and inversely as the square of
the individual’s height in inches. A person who weights 118 pounds and is 64 inches
tall has a BMI of 20. (the BMI is rounded to the nearest whole number.) Find the
BMI of a person who weights 165 pounds with height 70 inches.
a) Write the equation
b) Solve the problem
Determine whether x and y show direct variation, inverse variation, or neither. If it’s
direct or indirect variation, write the equation relating x and y.
22.
24.
X
Y
X
Y
1
10
90
3
4
9
80
2
7
8
70
1
X
Y
X
Y
9
3
75
15
11
5
85
10
13
7
90
5
23.
25.