FRAMING A FORMULA- PROBLEM & SOLUTION
There are some sample of framing formula -
Example-1)
1) Richard’s age is just 1/3rd of his father’s age, so find out the relations -
Ans.) Suppose the age of Richard implies by ‘S’ and the age of his father is implies by ‘F’, so the formula must be F / 3 = S, or F = 3S.
2) If Michel is 6 years elder than thrice of his sister, then form a relation
Ans. As per the given condition, it has been seen that, Michel is 6 years elder than thrice of his sister,
If the age of Michel is implied by ‘M’ and the age of his sister is implied by ‘S’
Then, the desired calculation/formula will be described by M = 6 + 3S
3) In the formula C/5 = ( F – 32 ) / 9, make ‘F’ the subject of the formula
Ans.) C F - 32
----------- = -------------
5 9
Or, 9C = 5 ( F – 32 )
Or, 9C = 5F – 160
Or, 5F = 9C + 160
9C + 160
Or, F = ---------------
5
Or, F = 9/5 C + 32
Substitution –
When the literals in an algebraic expression are assigned particular values, the expression gets a particular value. This process is called substitution. The value of the expression obviously depends on the values substituted for the literals.
Example-1) Find the value of 5x + 8y – 6z, if x = 4, y = 5, z = 3
Ans.) Substituting the given value of x, y, z.
5x + 8y – 6z = ( 5 X 4 ) + ( 8 X 5 ) – ( 6 X 3 )
= ( 20 + 40 ) – 18 = 42 (Ans.)
Example.2) Find the value of 3x – 7y + 9z ; if x = 7, y = 6, z = 6
Ans.) 3x – 7y + 9z = ( 3 X 7 ) – ( 7 X 6 ) + ( 9 X 6 )
= 21 – 42 + 54
= 33 (Ans.)
Substitution in a Formula –
To find the value of an unknown variable from a formula when the values of the other variables are known, we have to follow the below steps.
Step.1) First of all, we have to make the unknown variable as a subject of the formula.
Step.2) Then we have to substitute the values of the known variables in the formula and find the value of the subject.
Example.1) Suppose the speed of two cars are a & b respectively, if average ( A ) is = 20, and a = 30 then find b = ? Ans.) As per the given condition, the formula would be
a + b
A = ------------- , and let b = X
2
30 + X
20 = -------------- ,
2
40 = 30 + X ,
X = 40 - 30
X = 10
So, the value of b = 10 . (Ans.)
Example.2) If the diameter (d), of a circle = 2 x radius (r) , find r when, d = 20.
Ans.) as per the given condition d = 2 r ,
20 = 2 X r
r = 2 (Ans.)