What number when decreased by 9% becomes 36,400? (3marks)

If there are 20 poles along one side of a road, the number of spaces between them is one less than the number of poles.
Number of intervals $= 20 - 1 = 19$.

Each interval is $5 \text{ m}$ long.
Total distance $= \text{Number of intervals} \times \text{Distance per interval}$.
Total distance $= 19 \times 5 \text{ m} = 95 \text{ m}$.
The distance of the road is $\boxed{95 \text{ m}}$.

Question 23:

Cost Price (CP) $= 10,000 \text{ Frw}$.
Selling Price (SP) $= 12,500 \text{ Frw}$.
Profit $= \text{SP} - \text{CP} = 12,500 \text{ Frw} - 10,000 \text{ Frw} = 2,500 \text{ Frw}$.

Percentage Profit $= \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\%$.
Percentage Profit $= \left(\frac{2,500 \text{ Frw}}{10,000 \text{ Frw}}\right) \times 100\%$.

Percentage Profit $= \frac{1}{4} \times 100\% = 25\%$.
Her percentage profit was $\boxed{25\%}$.

Question 24:
To check for divisibility by 11, we use the rule: find the alternating sum of the digits (starting from the rightmost digit, subtract the next, add the next, and so on). If the result is divisible by 11, the number is divisible by 11.

• a) 64,737: $7 - 3 + 7 - 4 + 6 = 13$. (Not divisible by 11)
• b) 66,858: $8 - 5 + 8 - 6 + 6 = 11$. (Divisible by 11)
• c) 565,798: $8 - 9 + 7 - 5 + 6 - 5 = 2$. (Not divisible by 11)
• d) 232,467: $7 - 6 + 4 - 2 + 3 - 2 = 4$. (Not divisible by 11)

The number exactly divisible by 11 is $\boxed{\text{66,858}}$.

Question 25:

Let the original number be $x$.
When the number is decreased by $9\%$, it means it becomes $100\% - 9\% = 91\%$ of its original value.
So, $91\%$ of $x$ is 36,400.
$0.91x = 36,400$.

$x = \frac{36,400}{0.91}$.
$x = \frac{36,400}{\frac{91}{100}}$.
$x = \frac{36,400 \times 100}{91}$.

$x = 400 \times 100 = 40,000$.
The number is $\boxed{40,000}$.

Question 26:

$225 \times 1.24 = 279$.
So, the quantity is $279 \text{ hl}$.

We know that $1 \text{ hl} = 10 \text{ dal}$.
$279 \text{ hl} = 279 \times 10 \text{ dal} = 2790 \text{ dal}$.
The result is $\boxed{2790 \text{ dal}}$.

Question 27:

The sequence is $25, 18, 11, 4, \dots$.
$18 - 25 = -7$.
$11 - 18 = -7$.
$4 - 11 = -7$.
The common difference is $-7$.

The next number after 4 is $4 - 7 = -3$.
The number after $-3$ is $-3 - 7 = -10$.
The missing numbers in the sequence are $\boxed{-3, -10}$.

Question 28:

We can use long division.
$1564 \div 251 = 6$ with a remainder. ($6 \times 251 = 1506$)
$1564 - 1506 = 58$. Bring down 7, making it 587.
$587 \div 251 = 2$ with a remainder. ($2 \times 251 = 502$)
$587 - 502 = 85$. Bring down 3, making it 853.
$853 \div 251 = 3$ with a remainder. ($3 \times 251 = 753$)
$853 - 753 = 100$. Bring down 4, making it 1004.
$1004 \div 251 = 4$ with no remainder. ($4 \times 251 = 1004$)
The result of the division is $\boxed{6234}$.

Question 29:

• a) Name above figure: The figure shown is a three-dimensional shape with six square faces. The name of the figure is a $\boxed{\text{Cube}}$.

• b) How many edges does above figure have? A cube has 12 edges. The figure has $\boxed{12}$ edges.

• c) How many vertices does above figure have? A cube has 8 vertices (corners). The figure has $\boxed{8}$ vertices.

• d) If the side of above figure is $5 \text{ cm}$, work out its area.

For a cube, this typically means the total surface area.
A cube has 6 identical square faces.