Ratio

S03 paper 2 question 5

The ratios of teachers : male students : female students in a school are 2 : 17 : 18.

The total number of students is 665.

Find the number of teachers. 

Solution 1:\[\frac{665}{(17 + 18)} \times 2 = 38\]
Solution 2: \[\ teacher (ratio) : teachers + students  (ratio) = x (numbers): teachers + students (numbers)\]
\[\ 2:(2+17+18) = x : 665\]
\[\ 2:37 = x : 665\]
\[\frac{2}{37} = \frac{x}{665}\]
\[\ x = \frac{2}{37} \times 665\]
\[\ = 38\] 
Explaination for solution 1: 
total parts of students (males and females) = 35 parts  (17+18)
total parts of teachers  = 2 parts
35 parts of students are made up of 665 number of students, so each part contains 19 students :
\[\frac{665}{35}  =  19 \]
so, 2 parts of teachers are made up of  38
\[19  \times 2 = 38\]

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S04 paper 2 Question 19
The area of triangle APQ is 99 cm2 and the area of triangle
ABC is 11 cm2. BC is parallel to PQ and the length of PQ is 12 cm.

Calculate the length of BC.







Solution : \[\triangle ABC (area) : \triangle APQ (area) = 11cm^{2}  : 99 cm^{2} \]

change area ratio to linear ratio \[\ 11cm^{2}  :  99cm^{2} =  \sqrt{ 11cm^{2} }  :  \sqrt{ 99cm^{2} }\]

\[\Rightarrow  \sqrt{ \frac{11}{99} } = \frac{BC}{12}\]
\[\Rightarrow  \sqrt{ \frac{1}{9} } = \frac{BC}{12}\]
\[\Rightarrow  \frac{1}{3} \times 12 = BC\]
\[\Rightarrow  BC = 4\]



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S04 paper 4 Question 1(d)( i )

Fatima and Mohammed are members of a school team which takes part in a bike ride for charity.

Fatima and Mohammed ride a total distance of 36 km.
The ratio distance Fatima rides : distance Mohammed rides is 11 : 9.
Work out the distance Fatima rides.
Solution 1:\[\frac{36}{(11+9)} \times 11 = 19.8\]
Solution 2: \[\ Fatima rides (x) : Mohammed rides(y) = 11: 9\]
=> \[\ x : y = 11: 9\]=> \[\frac{x}{y} = \frac{11}{9}\]
=>\[\ 9x = 11y  (equation- 1)\]
 Total distance travel by Fatima and Mohammed \[\ x+y =36\]
=>\[\ y=36-x (equation- 2)\]
Substitute equation- 2 into equation-1 \[\ 9x = 11(36-x)\] 
=>\[\ 9x =396 - 11x\]
=>\[\ 9x+11x =396\]
=>\[\ x = 19.8\]

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W05 paper 4 Question 1a, 1b
1(a) Hassan sells fruit and vegetables at the market.
The mass of fruit and vegetables he sells is in the ratio fruit : vegetables = 5 : 7.
Hassan sells 1.33 tonnes of vegetables. How many kilograms of fruit does he sell?

1(b) The amount of money Hassan receives from selling fruit and vegetables is in the ratio fruit : vegetables = 9 : 8.
Hassan receives a total of $765 from selling fruit and vegetables. Calculate how much Hassan receives from selling fruit.

Solution 1(a):\[\  fruit(f) : vegetables(v) = 5 : 7 = f : 1.33\]

=> \[\ 5 : 7 = f : 1.33\]

=> \[\frac{5}{7}= \frac{f}{1.33}\]

=> \[\ f = \frac{5}{7} \times 1.33 \]

=> \[\ f = 0.95 (tonnes) \]

convert to kg, 1 ton = 1000 kg

=> \[\ f = 0.95 \times 1000 \]

=> \[\ f = 950 (kg) \]

 

Solution 1(b): \[\  fruit(f) : vegetables(v) = 9 : 8 \]

Total parts fruit + vegetable

=> \[\ 9+8 =17 \]

Fruit money is 9 parts out of total (9+8 parts)

=> \[\frac{9}{9+8} \times 765 = 405 ($) \]

 

 

 

 

 

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