Since Kobby is 5 years older than his brother, his brother's age is 5 years less than that of Kobby's age.

Kobby is 13 years now.

Brother's age = 13 - 5
Brother's age = 8

Let x be the number

A certain number (x) is subtracted from 12 → result = 12 - x

The result is multiplied by 3 → (12 - x) x 3

The answer is 21 → (12 - x) x 3 = 21

Now solve for x

(12 - x) x 3 = 21

a(b - c) = a x b - a x c

(12 - x) x 3 = 12 x 3 - 3 x x

12 x 3 - 3 x x = 36 - 3x

36 - 3x = 21

Move the - 3x to the right side of the equation and 21 to the left

- 3x becomes 3x at the right (when negative crosses the equal to sign becomes positive

21 becomes -21 at the left

36 - 21 = 3x

15 = 3x

Divide both sides of the equation by 3 to make x the subject

15/3 = 3x/3

5 = x

∴ x = 5

You can verify

12 - 5 = 7 (Result)

7 x 3 = 21 (Answer)

The Cardinal Point

We can draw the diagram below from the above information

We can apply pythagoras theorem to calculate how far she was from her starting point

NOTE: the c is the longest part or the side faceing the right angle (90^o)

We can redraw our diagram to:

Now solve for the value of x

Take the square root of both sides to get ride of the square

Total pocket money given = 3 x 1.5 = GH₵ 4.5

Amount left = Initial Amount - Amount Given = 5 - 4.5 = GH₵ 0.5

Priscila's age = k

Mary's age = b

Mary is 15 years older than Priscila. This means that if you add 15 years to Priscila's age, you will get Mary's age or if you subtract 15 years from Mary's age you will get Priscila's age.

Mary's age = Priscila's age + 15

b = k + 15

Now let 15 be alone at the right hand side of the equation, thus move the k to the left hand side. Its positive(+) so it becomes negative (-)

b - k = 15

Amount Left = Total Amount Needed - (Amount contributed by the 12 towns + Amount contributed by the district assembly

Each (Each and every) community contributed GH₵ 25,000.00, to get the total amount contributed by the communities, you have to multiply the amount contributed by each by 12 (Total number of communities which contributed)

Amount contributed by the community = GH₵ 25,000.00 x 12 = GH₵ 300,000.00

Total amount contributed = Amount contributed by the communities + Amount contributed by the District Assembly

Total amount contributed = GH₵ 300,000.00 + GH₵ 30,500.00 = GH₵ 330,500.00

Amount left for the project = Total Amount Needed - Amount Contributed

Amount left for the project = GH₵ 375,000.00 - GH₵ 330,500.00 = GH₵ 44,500.00

Cost for buying 5 units of brand S = 5 x GH₵ 3,000.00
Cost for buying 5 units of brand S = GH₵ 15,000.00

Cost for 5 units of brand T = 5 x GH₵ 4,000.00
Cost for 5 units of brand T = GH₵ 20,000.00

Amount saved = Cost for buying 5 units of brand T - Cost for buying 5 units of brand S
Amount saved = GH₵ 20,000 - GH₵ 15,000
Amount saved = GH₵ 5,000.00

Joyce is thrice as old as Mensah means when you multiply Mensah's age by 3, you should get Joyce's age

Joyce's age = 3 x Mensah's age = 3 x 5 = 15 years

Let y = the number of years that Joyce age will be twice as old as Mensah

In y years time,

Mensah's age = 5 + y

Joyce's age = 15 + y

When Joyce is twice as old as Mensah:

15 + y = 2(5 + y)

15 + y = 10 + 2y

15 - 10 = 2y - y

5 = y

Method I

Using proportionality

The total fraction is 1

Fraction of learners who failed + Fraction of learners who passed = 1

Fraction of learners who failed = 1 - Fraction of learners who passed

Fraction of learners who failed = 1 - $\frac{2}{3}$

Every whole number is being divided by 1 but it is not written.

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

Fraction of learners who failed = $\frac{1}{1}$ - $\frac{2}{3}$

Fraction of learners who failed = $\frac{\mathrm{1\; x\; 3\; -\; 2\; x\; 1}}{3}$

Fraction of learners who failed = $\frac{\mathrm{3\; -\; 2}}{3}$

Fraction of learners who failed = $\frac{1}{3}$

Number of learners who failed = 69

If $\frac{1}{3}$ = 69

$\frac{2}{3}$ = $\frac{2}{3}$ x 69 ÷ $\frac{1}{3}$

$\frac{2}{3}$ = $\frac{2}{3}$ x 69 x $\frac{3}{1}$ = $\frac{\mathrm{2\; x\; 69\; x\; 3}}{\mathrm{3\; x\; 1}}$ = 2 x 69 = 138

Alternatively,

Treating the fractions as parts:

$\frac{2}{3}$ can be seen as the class being divided into 3 parts

Total parts = 3

Passed parts = 2

Failed parts = 3 - 2 = 1

Now use the proportionality rule

If 1 part = 69

2 pars = $\frac{\mathrm{2\; x\; 69}}{1}$ = 2 x 69 = 138

∴ 138 learners passed

Method II

Representing the total number of learners by a variable and solve for it.

Let n = number of learners

of means multiplication

$\frac{2}{3}$ of learners passed means

Learners who passed = $\frac{2}{3}$ x n = $\frac{\mathrm{2n}}{3}$

Total number of learners = Number of learners who failed + Number of learners who passed

Number of learners who failed = Total number of learners - Number of learners who passed

But:

Total number of learners = n

Number of learners who passed = $\frac{\mathrm{2n}}{3}$

Number of learners who failed = n - $\frac{\mathrm{2n}}{3}$

But Number of learners who failed = 69

n - $\frac{\mathrm{2n}}{3}$ = 69

Solve for n

Get rid of the fraction by multiplying both sides by the denominator, 3

n x 3 - $\frac{\mathrm{2n}}{3}$ x 3 = 69 x 3

3n - 2n = 69 x 3

n = 69 x 3

Note: Since calculators are not allowed, leave the multiplication as it is for easier cancellation later.

But number of learners who passed = $\frac{\mathrm{2n}}{3}$

Number of learners who passed = $\frac{\mathrm{2\; x\; 69\; x\; 3}}{3}$ = 2 x 69 = 138

Alternatively,

3n - 2n = 69 x 3

n = 69 x 3 = 207

Total number of learners = 207

Number of learners who passed = Total number of learners - Number of learners who failed

Number of learners who passed = 207 - 69 = 138

Total number of oranges shared = Number of learners x Number each received

Total number of oranges shared = 42 x 11

Note: for easy cancellation later, leave the multiplication as it is.

Since 22 learners shared the same number of oranges:

Oranges shared by the 22 learners = 42 x 11

Number received by each learner = $\frac{\mathrm{Total\; number\; of\; oranges}}{\mathrm{Number\; of\; learners}}$

Number received by each learner = $\frac{\mathrm{42\; x\; 11}}{22}$ = 21

Notes:

1. 11 divides itself 1 time and 22, 2 times
2. 2 divides itself 1 and 42, 21
3. 21 x 1 = 21

Total birds = 150

Birds sold = 26

Birds kept = 150 - 26 = 124

Number of cages = 4

Birds in each cage = $\frac{\mathrm{Birds\; kept}}{\mathrm{Number\; of\; cages}}$ = $\frac{124}{4}$ = 31

Product means multiplication.

Let the third number be y.

6 x 3 x y = 90

18y = 90

Divide both sides by 18

y = $\frac{90}{18}$

y = 5