Easy ratio maths! help

Help me with the easiest answer.

1. If x:3 = 12 : x, calculate the positive value of x(how do i do this sort of maths)
2.If y:18= 8:y, calculate the positive value of y.
3. A cake weighing 550 g has three ingredients : flour , sugar and raisins. There is twice as much flour as sugar and one and a half times as much sugar as raisin . How much flour is there ?

thanks in advance

1. x:3 = 12:x

What I did was to write it in a fraction form. You'll get:

x/3 = 12/x

Cross multiply and you'll get: x^2 = 36
Find the square root of both sides and you'll get: x = 6

To check: 6:3 = 12:6
6/3 = 12/6
2=2

2. y:18=8:y

Do the same thing as above:
: y/18 = 8/y
: y^2 = 144
: y = 12

Check:
: 12/18 = 8/12
: 2/3 = 2/3

(I hope you're getting it so far. It's just basic.)

3. First you do representation

Flour - 2(1.5x) ("twice as much flour as sugar") or 3.0x
Sugar - 1 1/2x or 1.5x ("one and a half times as much sugar as raisin")
Raisins - x

Since it's a mixture all you have to do is add them and look for x.

3.0x + 1.5x + x = 550g
5.5x = 550g
x = 100g


Flour = 2(1.5x) = 3.0x = (3.0)(100) = 300g
Raisins = x = 100g
Sugar = 1.5x = 1.5(100) 150g

Add them up: 300 + 100 + 150 = 550g which means it's correct.

BUT, since the question is asking for the amount of flour ONLY. The answer will be 300g of flour.


Good luck!

x:3 is the same as x/3.
so, x/3=12/x; rearrange gives x^2=36. square root of 36 is 6 (or -6 but that isn't a positive value obviously). same method with question 2 (x^2=144).

question 3 is a multiple equations with multiple unknowns example.

x+y+z=550
x=2y
y=1.5z

substitute from the bottom two equations into the top one, and solve for x (x represents the amount of flour, y=sugar, z=raisin). That is, replace the z and y in the first equation with equivalent terms of x,