A number increased by 36 is equal to ten times itself. Class 7

A number increased by 36 is equal to ten times itself. Class 7

Question 1.

A number increased by 36 is equal to ten times itself. What is the number?

Solution:

Let the number be x.

So, x + 36 = 10x

or 9x = 36 or x = [latex]\frac {36}{9}[/latex] = 4.

Question 2.

Solve these equations :

(a) 5(r + 2) = 10

Solution:

5(r + 2) = 10

or 5r + 10 = 10 or 5r = 0, i.e.,

(b) - 3(u + 2) = 2(u - 1)

Solution:

-3 (u + 2) = 2(u - 1)

or - 3u - 6 - 2u - 2

or - 3u - 2u = -2 + 6

or u = -[latex]\frac {4}{5}[/latex]

(c) 2(7 - 2n) = -6

Solution:

2(7 - 2n) = - 6

or 14-4 n = - 6

or 4 n = 14 + 6 = 20

So, n = [latex]\frac {20}{4}[/latex] = 5.

(d) 20(x - 4) = - 16

Solution:

2(x - 4) = -16

or 2x - 8 = -16

or 2x = - 8

i.e., x = -[latex]\frac {8}{2}[/latex] = -4

(e) 6(x - 1) = 2(x - 1) - 4

Solution:

6(x - 1) = 2(x - 1) - 4

or 6x - 6 = 2(x - 1) - 4

or 6x - 2x = -2 - 4 + 6

or 4x = 0 i.e., x = 0.

(f) 3 - 7s = 7 - 3s

Solution:

3 - 7 s = 7 - 3s

-7s + 3s = 7 - 3

or - 4s = 4 i.e., s = [latex]\frac {4}{-4}[/latex] = -1.

(g) 2x + 1 = 6 - (2x - 3)

Solution:

2x + 1 = 6 - (2x - 3)

or 2x + 1 = 6 - 2x + 3

or 2x + 2x = 6 + 3 - 1

or 4x = 8 i.e., x = [latex]\frac {8}{4}[/latex] = 2.

(h) 10 - 5x = 3(x - 4) - 2(x - 7)

Solution:

10 - 5x = 3(x - 4) - 2(x - 7)

or 10 - 5x = 3x - 12 - 2x + 14

or - 5x - 3x + 2x = -12 + 14 - 10

or - 6x = - 8

= [latex]\frac {-8}{-6}[/latex] = [latex]\frac {4}{3}[/latex]