Can anyone help with my ratio homework?

Question

I don't get these questions. Can someone explain how to work it out please?

5. To make concrete you can mix 3 parts sand to 1 part cement. How much sand do you need to make 8 tonnes of concrete?

6. To make grey paint you can mix 3 parts black paint with 7 parts white paint. How much of each coloured paint do you need to make 20 litres of grey paint?

8. An alloy weighing 210g consists of copper, zinc and iron. There is three times as much copper as zinc and one and a half times as much zinc as iron. How much zinc is there?



Please be serious about this because this homework goes towards my ppm results.

Answer 1

IN 4 PARTS CONCRETE YOU HAVE 3S+1C.
IN 8 PARTS YOU HAVE 6S+2C.

IN 10 PARTS OF GRAY APINT YOU HAVE 3B+7W,IN 20 YOU TAKE 6B+14W.

1IRON+1.5 ZINC+4.5 COPPER=7

30X7=210 SO 30 IRON + 45 ZINC+ 135 COPPER.

Answer 2

The 8 tonnes of concrete must consist of 3 parts sand and 1 part cement. That's a total of 4 parts. So each part must be 8/4 = 2 tones. So the 3 parts sand will be 3 x 2 = 6 tonnes and 1 part cement will be 1 x 2 = 2 tonnes cement.


The grey paint consists of 3 parts black and 7 parts white paint, that's a total of 10 parts. Ten parts of 20 litres is 20/10 = 2 litres. So you will need 3 x 2 = 6 litres of black and 7 x 2 = 14 litres of white.

Start with 1 part of iron. There is 1.5 times as much zinc as iron so there will be 1 x 1.5 = 1.5 parts zinc. There is 3 times as much copper as zinc so there will be 3 x 1.5 = 4.5 parts copper.
hence in total we have 1 part iron, 1.5 parts zinc and 4.5 parts copper. That's a total of 7 parts. The 210 g consists of 7 parts so one part weighs 210/7 = 30 g. The zinc consists of 1.5 parts so this weighs 30 x 1.5 = 45 g

Answer 3

5. The total number of parts in the ratio is 3 + 1 = 4 parts

This means that 4 parts of the ratio = 8 tonnes

So the number of parts sand = 3/4 x 8 = 6 parts

Since 1 part = 8/4 = 2 tonnes

The number of tonnes of sand = 2 x 3 = 6 tonnes

6. As before total parts = 3 + 7 = 10 parts

1 part = 20 / 10 = 2L

So you need White => 7 x 2 = 14L

Black => 3 x 2 = 6L

Added together both come to 20L

7. Let: z = amount of zinc; c for copper; i for iron

1 part i + 1.5 parts z + 4.5 parts c = 7 parts

Therefore you have to times each number by 210/7 = 30

Iron = 1 x 30 = 30g

Copper = 4.5 x 30 = 135g

Zinc = 1.5 x 30 = 45g

Answer 4

5. The ratios are 3:1 :: Sand(S) : Cement(C)

Add the ratios 3 + 1 = 4
Divide 8 tonnes by 4 ( This gives one ratio) = 2 tonnes

So for 3 ratios of S, multiply 2 tonnes x 3 = 6 tonnes Sand
& for 1 Ratio of C, Multiply 2 tonnes x 1 = 2 tonnes Cement.

To check add the answers ( 6 tonnes + 2 tonnes = 8 tonnes) the required amount.

6. The ratios are 3 : 7 :: Black(B) : White (W)

Add the ratios 3 + 7 = 10

Divide 20 litres by 10 (This gives one ratio) = 2litres

So for 3 ratios of B multiply 2 litres x 3 = 6 litres.Black
& for 7 ratios of W multiply 2 litres x 7 = 14 litres White

(To check add the answers ( 6 litres +14 litres = 20 litres) the required amount).

8. Zinc : Iron :: 1.5 : 1
Copper : Zinc :: 3 : 1 ( This ratio (1) is equivalent to 1.5) So 3 must multiplied by 1.5 (3 x 1.5 = 4.5)
Combining the three elements:
Cu : Zn : Fe :: 4.5 : 1.5 : 1

Mathematicians don't like decimal numbers in the ratios, so in this case multiply through by 2
Cu : Zn : Fe:: 9 : 3 : 2

Now as before add the ratios 9 + 3 + 2 = 14

Divide 210 g by 14 (This gives one ratio) = 15 g

Zinc(Zn) is in the ratio of 3, so multiply 15 g x 3 = 45 g.

Answer 5

5) this is relatively straightforward. First, you work out what fraction of conctrete is sand. In this case it is 3/3+1 = 3/4. then, you times this by the amount of conncrete needed. In this case, it is eight tonnes. Therefore, you need 3/4 x 8 tonnes of sand, which works out at 6 tonnes

6) You do the same with this question. Grey paint is 3/10ths black and 7/10ths white. Therefore, you will need 3/10 x 20 of black paint (=6 litres), and 7/10 x 20 white paint (=14 litres).

7) O.k. this is the hard question. First, let us say the amount of iron is one. Copper will therefore equal 1.5 (1x 1.5) and iron 4.5 (3x1.5) This gives us the ratio:

I : Z : C
1: 1.5: 4.5

Therefore zinc contributes 1.5/(1+1.5+4.5) which is 1.5/7. therefore, the amount of zinc in 210g will equal 1.5/7 time 210, which equals 45g.



remeber to put in units

Answer 6

The key is setting up the equations:

5. s + c = 8 tonnes, total weight
s = 3c, three times as much sand as cement

Use substitution: 3c + c = 8, 4c = 8, c = 2 tonnes, so s = 6 tonnes.

6. Total volume is b + w = 20 liters
3parts b, 7 parts w:
there is 7/3 = 2.333 times as much w as b:

w = 2.333b

Use substitution: b + 2.333b = 20, 3.333b = 20, b=6 liters
Therefore, w = 14 liters.

8. Total weight of the three: c + z + i = 210g
c = 3z, z = 1.5i. Therefore set up the equation for i to get the other two:

c = 3(1.5i) = 4.5i

4.5i + 1.5i + i = 210
7i = 210

i = 30g
Therefore, z = 30 x 1.5i = 45g
c = 4.5 x 30i = 135g.

Check our work: c + z + i = 135g + 45g + 30g = 210g

I'm not the fastest, but I try to be the most thorough so you can learn how to do these.

Answer 7

5) You must assume that equal amounts of sand and cement weigh the same amount, or this problem cannot be solved.

So let x = amount of concrete
then 3x =amount of sand
so 4x = amount of concrete
4x =8 tons
x = 2 tons
3x = 6 tons = amount of sand

6) The total parts making grey paint is 3+7 =10.
Thus 3/10 of 20 = 6 litres of black paint
7/10 of 20 = 14 litres of white paint

8) Let x = amount of iron
then 1.5 x = amount of zinc
(3)(1.5x) = 4.5 x = amount of copper
Thus the alloy = x+1.5x + 4.5 x = 7x
Assuming that equal amounts of each metal weigh the same:
7x-210
x= 30
amount of zinc = 1.5x = 1.5(30) = 45 g

Answer 8

5. 3/1 X 8/8 = 24/8 24 parts sand

6. 3/7 X 20/20 = 60/140 60 black 140 white

7. i = x z = 1/2x c = 3/2x solve for x

Answer 9

5) How much does 3 parts sand to one part cement make???
one pound or one ton???
6) If 3 parts black paint with 7 parts white paint makes 1 litre and you need to make 20 litres: 3x20=60 and 7x20=140-thus 60-140
8) I can solve this algebretically....: c= 3z i=z divided by 2

I am not sure about 5 and 8 because i'm only 11-but I'm in advanced math.