(a)

Of means multiplication (x)

(b)

Acres of land for oranges = Acres of land for mangoes + 20

Acres of land for oranges = $\frac{\mathrm{2x}}{3}$ acres

Acres of land for mangoes = $\frac{\mathrm{x}}{4}$ acres

$\frac{\mathrm{2x}}{3}$ = $\frac{\mathrm{x}}{4}$ + 20

Solve for the value of x

Get rid of the denominators by multiplying both sides of the equation by the L.C.M of the denominators (3 and 4). The L.C.M is 12.

12 x $\frac{\mathrm{2x}}{3}$ = 12 x $\frac{\mathrm{x}}{4}$ + 12 x 20

4 x 2x = 3 x x + 240

Note: 3 divides itself once and 12, 4 times. 4 divides itself once and 12, 3 times.

8x = 3x + 240
8x - 3x = 240
5x = 240

Divide both sides of the equation by 5 so that x stands alone.

x = $\frac{240}{5}$

x = 48 acres

(c)

Acres of land for mangoes = $\frac{\mathrm{x}}{4}$ acres

x = 48

Acres of land for mangoes = $\frac{48}{4}$ acres

Acres of land for mangoes = 12 acres

(d)

Method I

Total acres of land = 48

Acres of land for oranges = $\frac{\mathrm{2x}}{3}$ acres

x = 48

Acres of land for oranges = $\frac{\mathrm{2\; x\; 48}}{3}$ acres

Acres of land for oranges = 2 x 16

Note: 3 divides itself once and 48, 16 times.

Acres of land for oranges = 32

Alternate

Acres of land for oranges = Acres of land for mangoes + 20

Acres of land for manges = 12

Acres of land for oranges = 12 + 20
Acres of land for oranges = 32

Total acres of land used = 12 + 32
Total acres of land used = 44

Land not used = 48 - 44
Land not used = 4

Percentage = $\frac{\mathrm{Number}}{\mathrm{Total}}$ x 100%

Percentage (not used) = $\frac{4}{48}$ x 100%

Percentage (not used) = $\frac{1}{12}$ x 100%

Note: 4 divides itself once and 48, 12 times.

Percentage (not used) = $\frac{\mathrm{1\; x\; 100}}{12}$%

Percentage (not used) = $\frac{100}{12}$%

Percentage (not used) = 8.33% ≈ 8 (nearest whole number)

100 divided by 12

	8.33
12	100 -96 40 -36 40 -36

Method II

The fraction of the entire acres of land is 1

Fraction for mangoes = $\frac{1}{4}$ x 1

Fraction for mangoes = $\frac{1}{4}$

Fraction for oranges = $\frac{2}{3}$ x 1

Fraction for mangoes = $\frac{2}{3}$

Total fractions used for the cultivation = $\frac{1}{4}$ + $\frac{2}{3}$

Total fractions used for the cultivation = $\frac{\mathrm{1x\; 3\; +\; 2\; x\; 4}}{12}$

Total fractions used for the cultivation = $\frac{\mathrm{3\; +\; 8}}{12}$

Total fractions used for the cultivation = $\frac{11}{12}$

Fraction not used = 1 - $\frac{11}{12}$

1 = $\frac{1}{1}$

Fraction not used = $\frac{1}{1}$ - $\frac{11}{12}$

Fraction not used = $\frac{\mathrm{1\; x\; 12\; -\; 11\; x\; 1}}{12}$

Fraction not used = $\frac{\mathrm{12\; -\; 11}}{12}$

Fraction not used = $\frac{1}{12}$

Percentage = Fraction x 100%

Percentage not used = $\frac{1}{12}$ x 100%

Percentage not used = $\frac{\mathrm{1\; x\; 100}}{12}$%

Percentage not used = $\frac{100}{12}$%

Percentage not used = 8.33% ≈ 8 (nearest whole number)

(i)

4 years ago = (x - 1) - 4

NOTE: ago is in the past so you have to subtract the years

4 years ago = x - 1 - 4

4 years ago = x - 5

(ii)

8 years from now = (x - 1) + 8

NOTE: from now is in the future so you have to add the years

8 years from now = x - 1 + 8

8 years from now = x + 7

(iii)

8 years time = three times his age 4 years ago

From (i)

8 years time = x + 7

4 years ago = x - 5

x + 7 = 3 x (x - 5)

x + 7 = 3 x x - 3 x 5

x + 7 = 3x - 15

Solve for x

7 + 15 = 3x - x

22 = 2x

Divide both sides by 2

22/2 = 2x/2

11 = x

x = 11

Since Fred is x - 1 years now, Fred's age now = 11 - 1 = 10

Fred is 10 years now