9.6 Task: Joint and Combined Variation

Last updated 8 months ago

12 questions

Note from the author:

For each problem find:
The constant of variation, k
The formula to express the relationship using that constant
The answer to the prediction question

- Write each fraction in parenthesis. 
- For complicated numerator or denominators write them in parenthesis too
- Use "^" for powers and "sqrt" for square roots.
- Don't leave any space

Instructions

For each problem find:
The constant of variation, k
The formula to express the relationship using that constant
The answer to the prediction question

- Write each fraction in parenthesis. 
- For complicated numerator or denominators write them in parenthesis too
- Use "^" for powers and "sqrt" for square roots.
- Don't leave any space

p is jointly proportional to q and r. If p = 12 when q = 6 and r = 4.
 a) Find the value of  k
b) Find the equation
c) What is p when q = 3 and r = 12

a)     k = _______
b)     p = _______
c)      p = _______  

The number of bags of grass seed n needed to reseed a yard varies directly with the area a to be seeded and inversely with the weight w of a bag of seed. If it takes two 3-lb bags to seed an area of 3600 ft2

a) Find the value of the constant k
b) Find the equation
c) How many 3-lb bags will seed 9,000 ft2?

a)    k = _______ 
b)    n = _______ 
c)    n = _______ 

e varies jointly as f and g. If e = 48 when f = 4 and g = 3
a) Find the value of k
b) Find the equation
c) What is the value of e when f = 7 and g = 8

a) k = _______ 
b) e = _______ 
c) e = _______ 

The number of students s varies jointly as the number of teachers t and the number of administrators a squared. 1000 students were present when there were 5 teachers and 2 administrators. 
a) Find the value of k 
b) Find the equation
c) How many students were there with 8 teachers and 1 administrator?

a) k = _______ 
b) s = _______ 
c) s = _______ 

a is jointly proportional with the square of x and the square root of y
a = 12 when x = 2 and y = 81

a) Find the equation
b) What is a when x = 4 and y = 9
 
a)    a = _______ 
b)    a = _______ 

The number of girls (g) varied directly as the number of boys (b) and inversely as the number of teachers (t). When there were 50 girls, there were 20 teachers and 10 boys. How many boys were there when there were 10 girls and 100 teachers?
 a) Find the equation
 b) How many boys were there when there were 10 girls and 100 teachers?

a)   g = _______ 
b)   b = _______ 

w is inversely proportional to the cube of x and to the square of y.
If w = 5 when x = 2 and y = 3
a) Find the equation
b) What is x when w = 10 and y = 6
 
a)   w = _______ 
b)   x = _______ 

The number of rabbits (b) varied directly as the number of squirrels (s) and inversely as the number of raccoons (c). When there were 10 rabbits and 40 squirrels there were only 2 raccoons.

a) Find the equation
b) How many raccoons went with 5 rabbits and 20 squirrels?

a)   b = _______ 
b)   c = _______ 

h is directly proportional to j and l.
h = 12 when j = 8 and l = 0.5
What is the value of l when h = 15 and j = 5

   l = _______

Horses vary directly as goats and inversely as pigs squared. When the barnyard contained 5 horses there were 4 pigs and only 2 goats. How many goats went with 6 pigs and 10 horses?

 g = _______

m is inversely proportional to n and to p.
If m = 1.8 when n = 2.1 and p = 2.
What is p when m = 2 and n = 4

 
 p = _______ 

The number of buckets of paint n needed to paint a fence varies directly with the total area a of the fence and inversely with the amount of pain p in a bucket. It takes three 1-gallon buckets of paint to paint 72 ft2 of fence. How many 1-gallon buckets will be needed to paint 90 ft2 of fence?

 n = _______