LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

FRAMING FORMULAE

__FORMULAE__

**A formula
is a relation between certain ****quantities****,
expressed with the help of variables and mathematical symbols.**

**Example.1****) When a
number is multiplied by 5 and 12 is deducted from the product, the result is 7
more than thrice the number, if we denote the number ‘x’, we can represent this
statement by the formula, 5x – 12 = 3x + 7**

**Example.2****) The
volume (V) of a cuboid is the product of its length (l), breadth (b), and
height (h). This can be expressed by the formula V = l X b X h.**

**Example.3****) The
area (A) of a rectangle is the product of its length (l) and its breadth (b).
This can be expressed as A = l X b. **

__Process of Framing a Formula –__

**Step.1)
Use variables such as a, b, c, d, w, x, y, z, etc. for the quantities for which
you want to frame the formula. Certain symbols are traditionally used to denote
certain variables.**

**Examples.
A) ‘V’ is used for volume, ‘A’ for area, ‘l’ for length, ‘b’ for breadth, ‘h’
for height, and ‘S’ for surface area in mensuration.**

**B) ‘v’
& ‘u’ are used for speed, ‘s’ for distance, and ‘t’ for time in physics.**

**C) ‘P’
is used for principal, ‘A’ for amount, ‘R’ for rate, ‘I’ for interest, and ‘T’
for time in arithmetic.**

**D) Use
the rules or conditions relevant to the context to establish a relationship
between the variables.**

**Example.1) Richard is 25 years older than his son Donald, after 10 years his age will be 7
years more than thrice the age of Donald. Frame a formula for these statements.**

**Ans.)
Let us assume the age of Donald is ‘x’ years**

**So, as
per the given condition, the age of Richard would be = x + 25**

**After 10
years the age of Donald would be = x + 10 **

**And,
After 10 years the age of Richard would be = ( x + 25 ) + 10**

**
= x + 35**

**Now, as
per the given condition, the required equation should be –**

** x
+ 35 = 3 ( x + 10 ) + 7**

**above
equation is the required formula. (****Ans.****)**

**Example.2)
In a three-digit number, the digit in the tens place exceeds the digit in the
units place by 7, and reduced the hundred place by 4, write the formula for the
number.**

**Ans.) Let
us assume that, the digit in the units place be ‘x’**

**Then the
digit in the tens place = x + 7**

**And, the
digit in the hundreds place = x - 4**

**So, the
number would be = 100 X digit in hundreds place + 10 X digit in tens place +
digit in unit place**

**
= 100.( x – 4 ) + 10.( x + 7 ) + x**

**
= 100x – 400 + 10x + 70 + x = ( 100 + 10 + 1 ).x – ( 400 –
70 )**

**
= 111x – 330****
(****Ans.****)**

**Example.3)
In all, 250 tickets were sold for a charity show. Adult tickets cost $ 20 each
and student tickets cost $ 10 each. If the number of adult tickets sold was x,
construct a formula for the income ‘I’ from the show.**

**Ans.)
As per the given situation, total of 250 tickets were sold and the number of
the adult ticket sold was ‘x’**

**So, the
number of student ticket was 250 – x**

**If the
cost of adult ticket was $ 20 each and the number of adult ticket sold was ‘x’,
so the total value came from the only adult ticket was = 20x**

**If the
cost of a student ticket is $ 10 and the number of students were 250 – x, then
the total value comes from only student ticket was = 10 ( 250 – x )**

**Now, if
‘I’ was the total income from the show –**

**
I =
20x + 10.( 250 – x )**

**
= 20x + 2500 – 10x = 10x + 2500****
(****Ans.****)**

**Example.4)
Steve has an average score of 58 runs in ‘x’ innings and an average of 65 runs
in ‘y’ innings, find the average score ‘A’ for ‘x’ & ‘y’ innings.**

**Ans.)
As per the given condition, Steve has an average score of 58 runs in ‘x’
innings**

**
So, the total runs scored in ‘x’ innings is = 58 X x = 58x**

**And,
Steve has an average score of 65 runs in ‘y’ innings**

**So, the
total number scored in ‘y’ innings is = 65y**

**so, total
runs scored by Steve = ( 58x + 65y )**

**Total
innings played by Steve is = ( x + y )**** 58x + 65y **

**So, the
equation of finding the average score is A = ------------ (****Ans.****)**

**
x + y**

**Example.5)
Pollard earns a profit of $ 300 by selling 15 toys at the rate of $ x per toy.
If the cost price of each toy is $ 40, frame a formula for the profit.**

**Ans.) as
per the given condition, the cost price is $ 40 for the 15 toys each.**

**So, the
total cost price of all the toys is = $ 40 X 15 = $ 600**

**Now,
Pollard sold out 15 toys at the cost of $ x per toys, so the total selling
price is $ 15x**

**Pollard
has earned a profit of $ 200**

**Now, as
per the given condition, the desired equation would be –**

**
15x – 600 =
300 **

**The above
equation is a required formula. (****Ans.****) **