Page 218 - Start Up Mathematics_6

Solution: Meena’s position is at step s

Beena’s position is at (s + 8)th step
Leena’s position is at (s – 7)th step
Difference between the steps of Beena and Leena = (s + 8) – (s – 7) = 15 steps
The total number of steps to the hilltop = 4s – 10

Example 18: During break, a school canteen contractor sells n cups of vanilla ice cream. What
may 2n represent? What may n represent?
3
Solution: 2n represents twice the number of students who like vanilla ice cream. n represents
3
one-third of the students who like vanilla ice cream. (Note: Answer may vary)
Example 19: Given Vani’s age to be x years, can you guess what (x + 3) may show? Can you
guess what (x – 5) may show? What is represented by 2x + 4?

Solution: Vani’s present age = x years
Thus (x + 3) shows her age after three years.
Thus (x – 5) shows her age 5 years ago.

Thus (2x + 4) shows the age of a person who is 4 years more than twice of Vani’s
age.
Example 20: Answer the following:

If Nikhil’s present age is x years, then determine:
(i) Nikhil’s age 3 years back.

(ii) Nikhil’s grandfather’s age who is five times Nikhil’s age.
(iii) Nikhil’s grandmother’s age who is 8 years younger to his grandfather.
(iv) Nikhil’s father’s age, who is 5 years more than 3 times Nikhil’s age.

Solution: Since Nikhil’s present age is x years, therefore
(i) Nikhil’s age 3 years back = (x – 3) years

(ii) Nikhil’s grandfather’s age = (5x) years
(iii) Nikhil’s grandmother’s age = (5x – 8) years

(iv) Nikhil’s father’s age = (3x + 5) years

Equation

An equation is a condition on a variable which is satisfied only for a definite value of a variable.
An equation contains an equality sign, i.e., ‘=’ between the two sides. In an equation, the value
of left hand side is equal to that of right hand side.
For example, an equation 3n = 21 is true for n = 7 only.
The value of the variable in the equation which satisfies the equation is called the solution of the
equation.

• The value n = 3 is a solution of the equation 2n + 4 = 10 as 2n + 4 = 2 × 3 + 4 = 10 but
n = 4 is not a solution of the given equation as 2n + 4 = 2 × 4 + 4 = 12 and not 10.
• The expressions (x + 4) > 21, (x – 1) ≤ 11 are not equations. These are known as inequalities.

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