Elementary Algebra, ratio word problems

In Elementary Algebra practice , a ratio expresses the magnitude of quantities relative to each other rather. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. Mathematically, a proportion is defined as the equality of two ratios. However in common usage the word proportion is used to indicate a ratio, especially the ratio of a part to a whole.Let's see an example from 4th grade math algebra word problems with solution

Question:-

Find two numbers such that their difference ,sum and product are in the ratio 1:4:15 respectively.

Answer:-

This solution will explain how to understand ratio word problems

Let the numbers be x and y

By the problem

(x-y) : (x+y) : (xy) = 1 : 4 : 15

x-y = k ----- 1

x+y = 4k ----- 2

xy = 15k -------- 3

Where k is the constant of proportionality

From 1+2 , we get x = 5k/2

Substitute this in eq 2 , we get y = 3k/2

By substituting this x and y values in eq 3

We get k = 4

If we put this k value in x = 5k/2 , we get x = 10

If we put k value in y = 3k/2 , we get y = 6

So the numbers are 10,6