ALGEBRA

 

If   1e  =  50; find the value of e.

      23

 

Solution

 

1e  =  50

23

 

¹23 x 1e  =  50 x  23     multiply by23 both sides.

       ₁23

 

1e = 50 x 23

 

e = 1150                   [because 1e = e]

 

hence e=1150

 

ZAMU YAKO

 

If   1d  =  20; find d.

     14

DEGREES B10

Find t in the figure below.

Solution

4t +  t + 90⁰ = 180⁰

5t = 180⁰ - 90⁰

5t = 90⁰

5t = 90⁰       [dividing by 4 on both sides]

5       5

c = 18⁰

DEGREES B9

Find c in the figure below.

Solution

2c +  c + 90⁰ = 180⁰

3c = 180⁰ - 90⁰

3c = 90⁰

3c = 90⁰       [dividing by 4 on both sides]

3       3

c = 30⁰

DEGREES B8

Find a in the figure below.

Solution

3a + 123⁰ = 180⁰

3a = 180⁰ - 123⁰

3a = 117⁰

3a = 117⁰       [dividing by 4 on both sides]

3       3

a = 39⁰

RATIOS C8

If 2: 8 = 10 : m; Find the value of m.

Solution

2   =  10                            [cross multiply]

8        m

2 x m = 10 x 8

2m = 80

2m = 80                      [divide by 2 on both sides]

2        2

m = 40

Hence the value of m is 40

TRY THIS…………

If 8:3 = 11: w; Find the value of w.

DEGREES B7

Find m in the figure below.

Solution

3m + m + 96⁰ + 108⁰ = 360⁰

4m + 204⁰ = 360⁰  [collecting like terms]

4m = 360⁰ - 204⁰

4m = 156⁰

4m = 156⁰       [dividing by 4 on both sides]

4        4

m = 39⁰

RATIOS C7

If 7: 5 = 14:B; Find the value of B.

Solution

7   =  14                            [cross multiply]

5        B

7 x B = 5 x 14

7B = 70

7B = 70                      [divide by 7 on both sides]

7        7

B = 10

Hence the value of B is 10

TRY THIS…………

If 7:2 = 14: c; Find the value of c.

DEGREES B7

Find a in the figure below.

Solution

2a + 80 = 180⁰

2a = 180⁰ - 80⁰

2a = 100⁰

2a = 100⁰       [dividing by 4 on both sides]

2       2

a = 50⁰

ALGEBRA B59

Simplify 20(4k)

Solution

 =20(4k)

=20 x 4 x k

=(20 x 4) x k

=(80) x k

=80k

Hence 20(4k) = 80k

TRY THIS…………

Simplify 18(5e)

RATIOS C6

If 3: 5 = 9:h; Find the value of h.

Solution

3   =   9                            [cross multiply]

5        h

3 x h = 5 x 9

3h = 45

3h = 45                      [divide by 3 on both sides]

3        3

h = 15

Hence the value of h is 15

TRY THIS…………

If 8:4 = 14: c; Find the value of c.

DEGREES B5

Find a in the figure below.

Solution

3a + 72 = 180⁰

3a = 180⁰ - 72⁰

3a = 108⁰

3a = 108⁰       [dividing by 4 on both sides]

3       3

a = 36⁰

DEGREES B6

Find a in the figure below.

Solution

3a + 81 = 180⁰

3a = 180⁰ - 81⁰

3a = 99⁰

3a = 99⁰       [dividing by 4 on both sides]

3       3

a = 33⁰

RATIOS C5

If 7: 5 = 14 : B; Find the value of B.

Solution

7   =  14                            [cross multiply]

5        B

7 x B = 5 x 14

7B = 70

7B = 70                      [divide by 7 on both sides]

7        7

B = 10

Hence the value of B is 10

TRY THIS…………

If 10:4 = 14: y; Find the value of y.

ALGEBRA B58

Simplify 20p + 6m + 5m + 7p

Solution

=20p + 6m + 5m + 7p

=20p + 7p  + 6m + 5m ( collecting the like terms)

= 27p + 11m ( adding the like terms)

Hence 10p + 5m + 2m + 7p = 27p + 11m

TRY THIS………………..

Simplify 20p + 7m + 8m + 9p

RATIOS C4

If 6: 5 = 18 : B; Find the value of B.

Solution

6   =  18                            [cross multiply]

5        B

6 x B = 5 x 18

6B = 90

6B = 90                      [divide by 6 on both sides]

6        6

B = 15

Hence the value of B is 15

TRY THIS…………

If 7:4 = 14: c; Find the value of c.

DEGREES B4

Find a in the figure below.

Solution

3a + a + 160 + 40 = 360⁰

4a + 200⁰ = 360⁰  [collecting like terms]

4a = 360⁰ - 200⁰

4a = 160⁰

4a = 160⁰       [dividing by 4 on both sides]

4       4

a = 40⁰

RATIOS C3

If 6: 5 = 10 : W; Find the value of W.

Solution

6   =  10                            [cross multiply]

5        W

6 x W = 5 x 10

6W = 50

6W = 50                      [divide by 6 on both sides]

6        6

W = 8²/6

Hence the value of W is 8²/6

TRY THIS…………

If 9:3 = 14: c; Find the value of c.

BODMAS B5

Find the value of 30 – 100 ÷ 20 x 2

Solution

Here we use BODMAS

1st we divide, then we multiply, lastly we subtract.

= 30 – 100 ÷ 20 x 2

=  30 – 5  x 2 (after dividing)

= 30 – 10 (after multiplication)

= 20    (then we get 20 after subtraction)

TRY THIS…………………………………

Find the value of 120 – 64 ÷ 8 x 8

DEGREES B3

Find a in the figure below

Solution

3a + 72 + 30 = 180⁰

3a + 102⁰ = 180⁰  [collecting like terms]

3a = 180⁰ - 102⁰

3a = 78⁰

3a = 78⁰       [dividing by 4 on both sides]

3       3

a = 26⁰

RATIOS C2

If 6: 8 = 11:B; Find the value of B.

Solution

6   =  11                            [cross multiply]

8       B

6 x B = 11 x 8

6B = 88

6B = 88                      [divide by 6 on both sides]

6        6

B = 14⁴/6 = 14²/3

Hence the value of B is 14²/3

TRY THIS…………

If 7:2 = 11: h; Find the value of h.