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1.

Set up equations and solve them to find the unknown numbers in the following cases: (a) Add 4 to eight times a number; you get 60. (b) One fifth of a number minus 4 gives 3. (c) If I take three fourths of a number and count up 3 more, I get 21. (d) When I subtracted 11 from twice a number, the result was 15. (e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8. (f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8. (g) Anwar thinks of a number. If he takes away 7 from `5/2` of the number, the result is `11/2`.

Answer» a) 8x+4=60
8x=56
x=7
b)`x/5-4=3`
`x/5=7`
x=35.
c)`3/4x+3=21`
`3/4x=18`
x=24
d)2y-11=15
2y=26
y=13
e)50-3x=8
3x=42
x=14
f)`(x+19)/5=8`
x+19=40
x=21
g)`5/2x-7=11/2`
`5/2x=25/2`
x=5.
Discussion
2.

Raju’s father’s age is 5 years more than three times Raju’s age. FindRaju’s age, if his father is 44 years old.

Answer» Let the age of Raju is `x` years. Then,
His father age ` = 3x+5` years
So, `3x+ 5 = 44`
`3x = 39=> x = 13`
So, Age of Raju is `13` years.
Discussion
3.

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)`

Answer» (a) `n+5 = 19`
For `n = 1`,
`1+5 = 19=> 6 = 19`, which is not true.
So, `n=1` is not a solution.

(b)`7n+5 = 19`
For ` n = -2`
`7(-2)+5 = 19=> -9 = 19`, which is not true.
So, `n=-2` is not a solution.

(c)`7n+5 = 19`
For ` n = 2`,
`7(2)+5 = 19=> 19 = 19`, which is true.
So, `n=-2` is a solution.

(d)`4p - 3 = 13`
For `p = 1`,
`4(1) -3 = 13=> 1= 13`
, which is not true.
So, `p = 1` is not a solution.

(e)`4p - 3 = 13`
For `p = 4`,
`4(4) -3 = 13=> 13= 13`
, which is true.
So, `p = 4` is a solution.

(f)`4p - 3 = 13`
For `p = 0`,
`4(0) -3 = 13=> -3 = 13`
, which is not true.
So, `p = 0` is not a solution.
Discussion
4.

Write the following statements in the form of equations:(i) The sum of three times x and 11 is 32.(ii) If you subtract 5 from 6 times a number, you get 7.(iii) One fourth of m is 3 more than 7.(iv) One third of a number plus 5 is 8.

Answer» (i) The sum of three times x and 11 is 32. `-> 3x+11 = 32`

(ii) If you subtract 5 from 6 times a number, you get 7. `->6x - 5 = 7`

(iii) One fourth of m is 3 more than 7.`-> 1/4m-7 =3`

(iv) One third of a number plus 5 is 8.`->1/3 x +5 = 8`
Discussion
5.

Write the following equations in statement forms: (i) `p + 4 = 15` (ii) `m - 7 = 3` (iii) `2m = 7` (iv) `m/5 = 3` (v) `(3m)/5 = 6` (vi) `3p + 4 = 25` (vii) `4p - 2 = 18` (viii) `p/2 + 2 = 8`

Answer» 1) p+4=15
p=11
2)m-7=3
m=10
3)2m=7
m=3.5
4)m/5=3
m=15
5)3m/5=6
m=10
6)3p+4=25
p=7
7)4p-2=18
p=5
8)p/2+2=8
p=12.
Discussion
6.

A shopkeeper sells mangoes in two types of boxes, one small and onelarge. A large box contains as many as 8 small boxes plus 4 loose mangoes.Set up an equation which gives the number of mangoes in each smallbox. The number of mangoes in a large box is given to be 100.

Answer» Let the number of mangoes in small box `= x`
Then, the number of mangoes in large box ` = 8x+4`
We are given, the number of mangoes in large box is `100`.
So, the required equation is,
`8x+4 = 100`
Discussion
7.

Solve: `x/30 - 1/33 = x/11 - 7/22`

Answer» `x/30-1/33=x/11-7/22`
`7/22-1/33=x/11-x/30`
`1/11(7/2-1/3)=(30x-11x)/(11*30)`
`(21-2)/6=(30x-11x)/30`
`19/6=19/30x`
`x=30/6`
`x=5`.
Discussion
8.

Write equations for the following statements:(i) The sum of numbers x and 4 is 9. (ii) The difference between y and 2 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 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

Answer» (i) The sum of numbers x and 4 is 9. `-> x+4 = 9`

(ii) The difference between y and 2 is 8.`-> y-2 = 8 or 2-y = 8`

(iii) Ten times a is 70.`-> 10a = 70`

(iv) The number b divided by 5 gives 6.`-> b/5 = 6`

(v) Three fourth of t is 15. `-> 3/4t = 15`

(vi) Seven times m plus 7 gets you 77.`->7m+7 = 77`

(vii) One fourth of a number minus 4 gives 4.`-> 1/4x-4 = 4`

(viii) If you take away 6 from 6 times y, you get 60.`-> 6y - 6 = 60`

(ix) If you add 3 to one third of z, you get 30. `->1/3z+3 = 30`
Discussion
9.

Solve the following:(a) 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. What is the lowest score?(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).(c) Smita’s mother is 34 years old. Two years from now mother’s age will be 4 times Smita’s present age. What is Smita’s present age?(d) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

Answer» 1)Lowest marks=x
2x+7=87
2x=80
x=40
2)a+a+40=180
2a=160
a=80
3)Smitas present age=x
4x=36
x=9
4)Rahuls score=x
Sachins score=2x
x+2x=198
3x=198
x=66
Rahuls score=66marksSachins score=132 marks.
Discussion