Page 152 - ICSE Math 6

Example 8: A man is 29 years older than his daughter. If the sum of their ages is 85 years, find their
present ages.
Solution: Let the age of daughter be x years. The man is 29 years older than his daughter. Therefore,
the age of the man is (x + 29) years.
As the sum of their ages is 85 years, therefore

x + (x + 29) = 85
⇒ 2x + 29 = 85
⇒ 2x = 85 – 29 = 56

56
⇒ x = = 28
2
Thus, the age of the daughter is 28 years and the age of the man is 28 + 29 = 57 years.

EXERCISE 13.2

1. If 13 is added to a number, the sum is 32. Find the number.

2. The sum of three consecutive numbers is 54. Find the numbers.
3. One third of a number when added to 5 gives 17. Find the number.
4. If 99 is added to 3 times of a number, it becomes 132. Find the number.
5. Raman subtracts 12 from a number and divides the difference by 7. If the quotient is 6 and there
is no remainder, find the number.

6. If a number is divided by 6, the quotient is 5 and the remainder is 3. Find the number.
 Number – Remainder 
 Hint : : = Quotient 
 Divisor 
7. The sum of two consecutive numbers is 43. Taking the bigger number as x, find the two numbers.
8. A girl is 6 years younger than her friend. If the sum of their ages is 34 years, find the age of
the girl.
9. A woman is 29 years older than her daughter. If the sum of their ages is 63 years, find their ages.
10. In a class, the number of boys are 5 less than the number of girls. Find the number of boys and
girls in the class, if there are a total of 35 students.

AT A GLANCE

¾ An equation is a mathematical statement which shows the equality of two expressions.
¾ A linear equation is an equation which consists of variables with highest power one.

¾ In an equation, equality does not change by adding, subtracting or multiplying both the sides of
the equation by the same quantity.

¾ In an equation, equality does not change by dividing both the sides of the equation by the same
non-zero quantity.
¾ A term on any side of the equation can be shifted to the other side by changing its sign. This is
known as transposition.
¾ A value of the variable which satisfies the given equation is known as the solution of the equation.

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