High School

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31.
a) Find the interior angle sum of a hexagon.

b) How many sides does a heptagon have?

c) Find the central angle of a regular pentagon.

32.
a) An amount of money gained an interest of 180,000 Frw. It was invested for 12 years. If the simple interest rate is 5%, calculate the principal amount.

b) Convert 6.85 into a fraction and show your work.

33.
a) Amina bought a laptop for 90,000 Frw and later sold it for 75,000 Frw.

i) Calculate her loss.

ii) Calculate the percentage loss.

b) Calculate the simple interest on 36,000,000 Frw at a 4% rate for 6 months.

34. John mixed 5 kg of high-quality rice with an unknown quantity of regular rice. The cost price of the mixture was 1,200 Frw per kg. High-quality rice costs 1,400 Frw per kg, and regular rice costs 1,000 Frw per kg when not mixed. Find the quantity of regular rice used.

Answer :

Let's address each part of the question step-by-step:

31. a) Find the interior angle sum of a hexagon.

A hexagon has 6 sides. The formula for finding the sum of the interior angles of a polygon is:

[tex](n - 2) \times 180^\circ[/tex]

where [tex]n[/tex] is the number of sides. For a hexagon:

[tex](6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ[/tex]

So, the interior angle sum of a hexagon is [tex]720^\circ[/tex].

31. b) How many sides does a heptagon have?

A heptagon is a seven-sided polygon. Therefore, a heptagon has 7 sides.

31. c) Find the central angle of a regular pentagon.

A regular pentagon has 5 equal sides and angles. The formula to find the central angle of a regular polygon is:

[tex]\frac{360^\circ}{n}[/tex]

where [tex]n[/tex] is the number of sides. For a pentagon:

[tex]\frac{360^\circ}{5} = 72^\circ[/tex]

So, the central angle of a regular pentagon is [tex]72^\circ[/tex].

32. a) An amount of money gained an interest of 180,000 Frw. It was invested for 12 years. If the simple interest rate is 5%, calculate the principal amount.

The formula for simple interest is:

[tex]\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]

Given:

  • Interest = 180,000 Frw
  • Rate = 5% = 0.05
  • Time = 12 years

We need to find the Principal (P):

[tex]180,000 = P \times 0.05 \times 12[/tex]

[tex]P = \frac{180,000}{0.05 \times 12}[/tex]

[tex]P = \frac{180,000}{0.6}[/tex]

[tex]P = 300,000 \text{ Frw}[/tex]

So, the principal amount is 300,000 Frw.

32. b) Convert 6.85 into a fraction and show your work.

To convert 6.85 into a fraction:

[tex]6.85 = \frac{685}{100}[/tex]

Now simplify:

The greatest common divisor of 685 and 100 is 5.

[tex]\frac{685 \div 5}{100 \div 5} = \frac{137}{20}[/tex]

So, 6.85 as a fraction is [tex]\frac{137}{20}[/tex].

33. a) Amina bought a laptop for 90,000 Frw and later sold it for 75,000 Frw.

i) Calculate her loss.

Her loss = Cost Price - Selling Price

[tex]90,000 - 75,000 = 15,000 \text{ Frw}[/tex]

ii) Calculate the percentage loss.

Percentage loss is calculated as:

[tex]\frac{\text{Loss}}{\text{Cost Price}} \times 100\%[/tex]

[tex]\frac{15,000}{90,000} \times 100\% = 16.67\%[/tex]

Amina's percentage loss is 16.67%.

33. b) Calculate the simple interest on 36,000,000 Frw at a 4% rate for 6 months.

Simple interest formula:

[tex]\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]

Here:

  • Principal = 36,000,000 Frw
  • Rate = 4% = 0.04
  • Time = 6 months = 0.5 years

[tex]\text{Interest} = 36,000,000 \times 0.04 \times 0.5[/tex]

[tex]\text{Interest} = 720,000 \text{ Frw}[/tex]

The simple interest is 720,000 Frw.

34. John mixed 5 kg of high-quality rice with an unknown quantity of regular rice.

Given:

  • Cost of high-quality rice: 1,400 Frw/kg
  • Cost of regular rice: 1,000 Frw/kg
  • Cost of the mixture: 1,200 Frw/kg

Let [tex]x[/tex] kg be the quantity of regular rice used.

The equation based on the cost is:

[tex]5 \times 1,400 + x \times 1,000 = (5 + x) \times 1,200[/tex]

[tex]7,000 + 1,000x = 6,000 + 1,200x[/tex]

Rearranging gives:

[tex]1,000x - 1,200x = 6,000 - 7,000[/tex]

[tex]-200x = -1,000[/tex]

[tex]x = 5 \text{ kg}[/tex]

So, John used 5 kg of regular rice.

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Rewritten by : Barada