Page 47 - Maths Skills - 7

Simple Equations 45

Example 4: Write an equation for the following situations:
(i) A shopkeeper sells mangoes in two types of boxes, one small and other large. A large box
contains as many as 8 small boxes plus 4 loose mangoes. Write an equation, if the number of
mangoes in the large box is given to be 100.
(ii) Sahil’s father is 48 years old. He is 17 years older than twice the Sahil’s age.

Solution: (i) Let the number of mangoes in small box be ‘m’. (ii) Let Sahil’s age be y years

Total mangoes = 100 ⇒ 8m + 4 = 100 Sahil’s father’s age = 48 years
⇒ 2y + 17 = 48

Exercise 3.1

1. Check whether the value given in the brackets is the solution or root of the given equation or not:

(i) n + 14 = 8 (n = – 6) (ii) 12a + 6 = 30 (a = – 2)
2
(iii) 3p – 7 = 15 (p = 2) (iv) 4m – 9 = (m = 1)
3
2. Write equations for the following statements:
(i) One third of a number plus 7 is 18. (ii) Five-sevenths of a number added to 3 gives –9.

(iii) Twice a number divided by 3 minus 2 gives 7. (iv) Four less than two-third of t is 21.
(v) 8 subtracted from three times ‘c’ is 4. (vi) If you take away 9 from 9 times z, you get 54.
3. Write the following equations in form of statements.

4p
(i) n + 9 = 13 (ii) = 15 (iii) 8m – 4 = 16
7 + p
4x x 5
(iv) – 7 = 0 (v) 5x = – 20 (vi) =
5 3 6
4. Write an equation for the following situations:

(i) Nikhil, who has 6 video games, has half as many games as Raj.
(ii) The 345 students who listed badminton as their favourite sport, were 13 less than two times the number
of students who listed basketball as their favourite sport.

(iii) Garima’s marks of 82 in her English test was 36 points less than twice the marks in her Science test.
(iv) Siddharth rode the roller coaster 7 times, which was thrice as many times as he rode the ferris wheel.
(v) The sum of two consecutive numbers is 23.

SOLVING AN EQUATION

Any linear equation in one variable can be solved using two methods:
Trial and Error Method
As the name says, we try substituting different values of the variable till the given equation is satisfied.
For example, 4n – 12 = 8
puting n = 0, LHS = 4 × 0 – 12 = 0 – 12 = – 12 putting n = 1, LHS = 4 × 1 – 12 RHS = 8

RHS = 8 = 4 – 12
Since, LHS ≠ RHS = – 8
Thus, n = 0 is not the solution. Since, LHS ≠ RHS
Hence, n = 1 is not the solution.