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6.  Set up an equation in the following cases:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit’s marbles.)
(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)
(iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.)
(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees).

(a) Let the Parmit's marbles be m. Then according to question we have :      or                                                                             (b)  Let the age of Laxmi be y years. Then we have :                              or                                                                (c)  Let the lowest marks be l, then :                                                    ...

5. Write the following equations in statement forms:

(i) p + 4 = 15

(ii) m – 7 = 3

(iii) 2m = 7

(iv) m /5 = 3

(v) 3 m/5  = 6

(vi) 3p + 4 = 25

(vii) 4p – 2 = 18

(viii) p /2 + 2 = 8

(i)  Add 4 to the number p, we get 15.  (ii) Subtract 7 from m to get 3. (iii)  Twice the number  m is 7.  (iv)   One-fifth of m is 3. (v)   Three-fifth of m is 6. (vi)  4 is added to thrice the number p to get 25.   (vii)  2 is subtracted from the product of 4 times p to get 18. (viii)  When 2 is added to half of the number p, we get 8.

4. Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.

(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.

(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.

(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30.

The equations are given below : (i)   (ii)   (iii)   (iv)        (v)           (vi)    (vii)      (viii)   (ix)     

3. Solve the following equations by trial and error method:
        (i) 5p + 2 = 17 (ii) 3m – 14 = 4

(i) Put p = 1, We have :      Put  p  = 2, We have :       Put p = 3, we have :       Thus the solution is p = 3.   (ii) Put m = 4, we have :     Put m = 5, we have :       Now, put m = 6, we have :        Thus m = 6 is the solution.

2. Check whether the value given in the brackets is a solution to the given equation  or not:

      (a) n + 5 = 19 (n = 1)

      (b) 7n + 5 = 19 (n = – 2)

      (c) 7n + 5 = 19 (n = 2)
      (d) 4p – 3 = 13 (p = 1)

      (e) 4p – 3 = 13 (p = – 4)

      (f) 4p – 3 = 13 (p = 0)

(a) Put n = 1 in the equation, we have :                            n  +  5  =  15  or                      1   + 5   = 15   or                            6       15 Thus n = 1 is not a solution.   (b) Put  n  =  - 2, we have :                           7n + 5 = 19 or                   7(-2)  + 5  =  - 14 + 5 = - 9   19. So, n = - 2 is not a solution to given equation.     (c) Put  n  =  2, we...

1. Complete the last column of the table.

      

The table is shown below :-                     
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