This document discusses solving problems involving joint variation. It begins by stating the learning objectives and targets, which are to solve problems involving variations and explain how to solve for unknown variable values. It then reviews that a statement of "a varies jointly as b and c" means the equation is a=kbc, where k is the constant of variation. An example problem is shown of finding a when b and c are given and the constant k is found using the initial values. Steps are provided to solve such problems: 1) write the correct variation equation, 2) use initial values to find k, 3) substitute k into the equation, 4) substitute all given values into the equation to find the unknown value. Several example problems are

1. Solve problem involving joint variation

2. LEARNING OBJECTIVES:
1. Solves problems involving
variations.

3. Learning TARGETS:
K –Translate mathematical
equation that describes the given
relation
U- Explain how to solve for
unknown values of variables

4. Review:
Translate the statement into
mathematical equation.
The amount of gasoline (L) used by a
motorboat varies jointly to the distance
(d) travelled and the square root of the
speed (s).

5. JOINT VARIATION
The statement “a varies jointly as
b and c” means a = kbc, where k is
the constant.

6. Solve problem
Example:
1. Find the equation of variation
where a varies jointly as b and c, and
a=36 when b=3 and c=4, find a when
b=5 and c=11.

7. Let us now solve the problem.
We can solve the problem using
these steps:
Step 1. Write the correct equation. Based
from the problem the equation is
a=kbc

8. Step 2. Use the information given in the problem to
find the constant of variation k.
a=kbc Given a=36 ,b=3 and c=4 Find k
36 = k(3)( 4)
36 = k(12)
12 12
3=𝑘
𝑘=3
Therefore, the required equation of variation is
a=3bc

9. Step 3. Rewrite the equation in step 1 and substitute
the value of k found in step 2.
a=3bc
Step 4. Substitute to the given equation the values
given in the problem.
Given: k=3, b=5 and c=11 Find a
a=(3)(5)(11)
a=(3)(55)
a=165

10. Solve for the value of the constant of
variation k, then find the missing value.
1. z varies jointly as x and y and z=60 when x=5 and y=6
A. find z when x=7 and y=6
B. find x when z=72 and y=4
C. find y when z=80 and x=4
2. The amount of gasoline (L) used by a motorboat varies
jointly to the distance (d) travelled and the square root of
the speed (s).
Suppose a motorboat used 25 liters on a 30
kilometer trip at 25 km/hr. How many liters will it use on a
42 kilometer trip at 49 km/hr?

11. 3. Wind resistance varies jointly as an object’s surface area
and velocity. If an object travelling 40 mile per hour with a
surface area of 25 square feet experiences a wind
resistance of 225 Newtons, how fast must a car with 40
square feet of surface area travel in order to experience a
wind resistance of 270 Newtons?
4. The mass of a rectangular sheet of wood varies jointly as
the length and the width. When the length is 20 cm and the
width is 10 cm, the mass is 200 grams. Find the mass when
the length is 15 cm and the width is 10 cm.
5. For a given interest rate, simple interest varies jointly as
principal and time. If Php 2000 left in an account for 4 years
earns Php 320. How much interest would be earned in if you
deposit Php 5000 for 7 years?

12. Activity
Solve the following:
1. z varies jointly as x and y. if z=3 when x=3 and y=15, find z
when x=6 and y=9.
2. The area A of a triangle varies jointly as the base b and the
altitude h of the triangle. If A=65 cm when b=10 and h=13,
find the area of a triangle whose base is 8 cm and whose
altitude is 11.
3. z varies jointly as x and y. z=60 when x=3 and y=4. find y
when z=80 and z=2.
4. d varies jointly as h and g. if d=15 when h=14 and g=5, find
g when h=21 and d=8.
5. z varies jointly as the square root of the x and y. if z=3 when
x=3 and y=12, find x when z=6 and y=64.

13. THANK YOU!!!!