8.1 Warm-Up Puzzle: Direct and Inverse Variation
Name: _______________________
Show your work for all problems! (The numbers are out of order on purpose!!!)
Part I: Each ordered pair is from a direct variation. Find the constant of variation.
1. (2, 4)
1
7. x = 6 when y 
1
2
2. (1, 5)
3. (100, 20)
8. x = 3 when y = 18
9. x = -10 when y = 11
Part II: Each ordered pair is from an inverse variation. Find the constant of variation.
4. (5.2, 0.25)
10. x = 0.2 when y = 2
5. (𝟐,
11. x 
1 7
−𝟏
𝟑
)
6.  , 
2 5
2
2
when y 
3
3
12. x 
9
2
when y  –
3
10
Part III: Each pair of values is from an inverse variation. Find the missing value.
13. (2, 6), (4, y)
14. (9, 2), (x, 3)
15. (7, 0.2), (5, y)
4 2 
5
16.  ,  ,  x, 
3 3  9
Part IV: Suppose that x and y vary inversely such that 𝑦 = −3 when 𝑥 = −10.
17. What is the value of x if 𝑦 = 6? _____________
18. What is the value of y if 𝑥 = −30? _____________
19. What is the constant of variation for this inverse relationship? ___________
Part V: The Puzzle! The solutions correspond to letters according to the table. The numbers below the
spaces correspond to the practice problem
number. Write the letter corresponding to the solution in each space.
“
’
”
- Bertrand Russell
(Mathematician and Philosopher)
Part VI: Real-Life Applications
#1) For a given speed, the distance traveled varies directly with time. Emma lives 5 miles from
school and Bryce lives 2 miles away. Bryce and Emma drive to school at the same speed.
IV: ____________________________
DV: ______________________
a) How long does it take Bryce to drive to school if it takes Emma 10 minutes?
b) How fast do they drive to school in miles per minute?
c) Write the rule for this situation using the appropriate variables (d distance, t time):
d) A new student Matt says it takes him 13 minutes to drive to school. Use your rule to
determine how far from school Matt lives.
#2) RBRO is raising money for a local charity by selling candy bars at lunch. They know there is
an inverse relationship between the price they charge per candy bar and the number of candy bars
they will sell. If they charge $1.50 per candy bar, they can expect to sell 200 candy bars.
IV: ____________________________
DV: ______________________
a) How does this situation reflect an inverse relationship? Be specific.
b) Write an equation (y = k/x) to model this situation.
c) How many fewer candy bars would they expect to sell if they charge $2 per candy bar?
Show your work!
d) How many more candy bars would they sell if they lowered the price to $0.50? Show your
work!