I've already answered most of these ques, i just need some1 to verify if they're correct.
1. A map is drawn to a scale of 1:50000. The distance between 2 places, A n B is 5cm on the map.
(a) Calculate the actual distance, in kilometres between A n B
1:50000= 1/50,000
1/50000*5
= 0.0001km
(b) 2 towns r 24km apart. Calculate in centimetres, their distance apart on the map.
24*10000
= 240000cm
(idk if its correct)
2.Given that 5cm on a map represents 4km on the ground;
(a) Calculate the distance in km, between 2 villages which r represented on the map by points 7.5cm apart
5/4*7.5
= 9.375km
(b) Express the scale of the map in the form 1:n
(idk what it means by that, so i didn't answer that 1)
3. A large swimming pool takes 36hours to fill using 3 identical pumps
(a) How long would it take to fill using 8 identical pumps?
3 pumps = 36hrs
1 pump = 36*2
= 108hrs
8 pumps = 108/8
= 27/2
= 13.5hrs
(b) If the pool needs 2 b filled in 9 hours, how many pumps will b needed?
108/9 = 12 pumps
4. A machine used to paint white lines on a road uses 250 litres of paint for each 8km of road marked. Calculate;
(a) How many litres of paint would b needed for 200km of road?
8km = 250L
1km = 250/8
= 31.25L
200km = 31.25*200
= 6250L
(b) What length of road could b marked with 4000 litres of paint?
4000/31.25 = 128km
5. A farmer plants 5 apple trees in 25 mins. If he continues to work at a constant rate, how long will it take him to plant 200 trees?
5 trees = 25 mins
1 tree = 25/5
= 5 mins
200 trees = 5*200
= 1000
= 16.6 hours
6. A teacher shares sweets among 8 students so that they get 6 each. How many sweets would they each have got had there been 12 students?
1 student = 6 sweets
12 students = 12/6
= 2 sweets each
7. Chairs in a hall are arranged in 35 rows of 18
(a) How many rows would there be with 21 chairs to a row?
(idk the answer 4 this)
(b) How many chairs would there be in each row if there were 15 rows?
15 rows = 15*21
= 315 chairs
8. Increase 200 in the ratio 8:5
8/5*200 = 320
9. Decrease 6000 in the ratio 3:5
3/5*6000 = 3600
10. Increase 4kg in the ratio 5:4
4*10000 = 40000g
5/4*40000 = 50000/10000
= 5kg
11. Decrease 210ml in the ratio 3:7
3/7*210 = 90ml
12. Decrease 30 in the ratio 5:8
5/8*30 = 75/4
= 18.75
plz check my answers n help me with the ones which i don't know. thank u
+118651 hi,
I really like that you have been prepared to answer them yourself and present your answers.
It means you are serious about learning :)
Lets look at Question 1
1. A map is drawn to a scale of 1:50000. The distance between 2 places, A n B is 5cm on the map.
(a) Calculate the actual distance, in kilometres between A n B
1:50000= 1/50,000
1/50000*5
= 0.0001km
(b) 2 towns r 24km apart. Calculate in centimetres, their distance apart on the map.
24*10000
= 240000cm
(idk if its correct)
I'll do it 2 different ways:
1st way
1:50000 means
1cm represents 50000cm so
1cm represents 500 m so
5cm represents 500*5 = 2500m
and
2500m = 2.5km
2nd way
\(\frac{1}{50000}=\frac{5}{d} \qquad \mbox{Note that all initial values are in cm}\\ \mbox{multiply both sides by 5000d}\\ \frac{1}{50000}\times \frac{50000d}{1}=\frac{5}{d}\times \frac{50000d}{1}\\ d=250000cm\\ d=250000\div 100 \;m\\ d=2500m\\ d=2.5km\)
+118651 Sorry, I didn't see part b
1. A map is drawn to a scale of 1:50000. The distance between 2 places, A n B is 5cm on the map.
(b) 2 towns r 24km apart. Calculate in centimetres, their distance apart on the map.
24*10000
= 240000cm
(idk if its correct)
2 towns are 24km apart
1 cm to 50000 cm becomes
1cm to 500 metres which is
2cm to 1 km
2*24cm to 1*24km
48cm represents 24km
Lets see if I can do this with algebraic fractions
I'd start with changeing 50000cm to km
50000 divided by 100 divided by 1000 = 0.5
so 1 cm represents 0.5km
\(\frac{1cm}{0.5km}=\frac{d\;cm}{24km}\\ \frac{1cm\times 24km}{0.5km}=\frac{d\;cm}{1}\\ \mbox{The km cancel out and you get}\\ \frac{24cm}{0.5}=d\\ d=48cm \)
So 24 km is represented by 48cm
Teachers teach these problems quite differently from one another and that tends to make it harder. ://
Have a look at the next one again yourself :// Then I will check it.
I have not looked at it at all yet . :(
Ok... um.. i've checked my answers n i'm pretty confident that most of them are ok.
But I still don't get number 2. (b) and number 7. (a)
plz help
n thank u 4 the answers for 1 (a) n (b) 
+118651 2.Given that 5cm on a map represents 4km on the ground;
(a) Calculate the distance in km, between 2 villages which r represented on the map by points 7.5cm apart
If you are going to do these as fraction equations, you need to learn to use the units properly.
See how I have done it with the km on the top of each fraction and the cm on the bottom.
When I solved the equation the equation the cm literally cancelled out! (There was one on the top of the fraction and one on the bottome of the fraction.)
\(\frac{d }{7.5cm}=\frac{4km}{5cm}\\ d=\frac{4km}{5cm}\times \frac{7.5cm}{1}\\ d=\frac{4*7.5km}{5}\\ d=6km\)
(b) Express the scale of the map in the form 1:n
(idk what it means by that, so i didn't answer that 1)
5cm represents 4km
You have to make the units the same so
5cm represents 4000m
5cm represents 400000cm
So the ratio is
5 : 400000
Divide both by 5
1 : 80000
+118651 7. Chairs in a hall are arranged in 35 rows of 18
35*18 = 630 chairs altogether
(a) How many rows would there be with 21 chairs to a row?
630/21 = 30 There would be 30 rows
(b) How many chairs would there be in each row if there were 15 rows?
630/15 = 42 chairs in each row :)
