# Solving Math Ratio Questions: Find the Answer (Option B)

• fork
In summary, the equations (x+y-z)/3 = (y+z-x)/4 = (z+x-y)/5 can be solved for x:y:z as 8:7:9. The first step is to multiply the ratios and then use the given equations to solve for x, y, and z. This can be done by substituting the known values for y and z into the first equation and solving for x. Then, using that value for x, solve for y and z in the same way. The resulting ratio is the solution for x:y:z. It is not necessary to use trial and error to find the solution.
fork
1)If (x+y-z)/3
=(y+z-x)/4
=(z+x-y)/5,
then x:y:z=
A.3:4:5
B.8:7:9
C.9:16:25
D.15:12:20

The answer for the above question is option B. But I don't know how to solve this kind of questions. Can anyone tell me what should I do in the first step? Thanks for answering my question.

step 1: 3*4*5=60
step 2: 20x+20y-20z=15y+...

Step2:20x+20y-20z=15y+15z-15x=12z+12x-12z
Step3:35x+32y=27y+35z=32z+27x

x=4(z-y)
y=7(z-x)
z=9(x-y)

That's what I solve from the above equation. After that, what should I do? Thanks.

Did you see AntonVrba's response? Since you asked to choose among different possible answers, the simplest thing to do is try each.
x= 3, y= 4, z= 5 ARE in ratio 3:4:5. Do those numbers satisfy the original equations?

If not try x= 8, y=7, z= 9, etc.

no need for trial and error of trying given posibilities, you can calculate
from the three relationships x,y,z that you already have solved by substituting first y and then for second z in the first of your equations.

x = 4z - 4y
= 4z - 28z + 28x
or
24z = 27x
8z = 9 x
8/9 = x/z or 8:9 = x:z

and

x = 4z - 4y
x = 36x - 36y - 4y
...

Yeah, but it works and thought it would be simpler for fork.

## What is a ratio?

A ratio is a comparison of two quantities, typically expressed as a fraction. It shows the relationship between the two quantities and can be written in different forms such as 1:2, 1/2, or 50%.

## How do I solve a math ratio question?

To solve a math ratio question, first identify the quantities being compared and write them as a fraction. Then, set up an equation using the given information and solve for the missing value using cross multiplication or equivalent ratios.

## What is Option B in a math ratio question?

Option B in a math ratio question refers to the second quantity being compared in the ratio. It is usually denoted by the letter "b" and can represent any numerical value or variable.

## Can ratios be simplified?

Yes, ratios can be simplified by dividing both the numerator and denominator by their greatest common factor. This will result in an equivalent ratio that is easier to work with.

## What are some real-life applications of ratios?

Ratios are used in many real-life situations, such as cooking (measuring ingredients), finance (calculating interest rates), and sports (statistics). They are also commonly used in business to compare financial data and make decisions.

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