the ratio between two distinct things

[Ryan$]

hi guys, lets assume I have a ration of 2:5 describe the ration of amount of cake vs amount of sugar respectively, so how much I need amount of sugar if I have amount of cake is 3, so what I have do is like this lets assume x is the amount of cake , y is the amount of sugar then
2*x :5 *y
3: < >

< > = (35y) / 2*x
so how do I know from what is written in <> the amount of sugar for making amount of cake 3?! thanks beforehand

 

[Otis]

… [ratio] 2:5 [describes] amount of cake vs amount of sugar …

I think it's better to say "to" instead of "vs".

2:5 denotes the ratio 2 parts cake to 5 parts sugar

… how much [sugar is needed if] amount of cake is 3 …

… [let's] assume x is the amount of cake …

You don't need symbol x for the amount of cake because you already said it's 3.

You can find the sugar amount by solving a simple proportion.

[MATH]\dfrac{2}{5} = \dfrac{3}{?}[/MATH]
Multiply on the diagonal and then divide by the number not used.

5 × 3 ÷ 2 = 7.5

You need 7.5 parts sugar for every 3 parts cake.

Check:

2/5 = 0.4
3/7.5 = 0.4

In other words, 2/5 = 3/7.5

 

[Otis]

Check out some lessons:

Writing proportions example

Some examples of writing two ratios and setting them equal to each other to solve proportion word problems.

www.khanacademy.org

Worked example: Solving proportions (video) | Khan Academy

Learn the reasoning behind solving proportions. We'll put some algebra to work to get our answers, too.

www.khanacademy.org

Ratios: What are They? How do They Work?

Ratios are straightforward: they are simply comparisons of two things, and they can be used to find per-unit rates and percentages. Learn more!

www.purplemath.com

Proportions

Proportion says that two ratios (or fractions) are equal

www.mathsisfun.com