Question

2 numbers are in the ratio 2:3 the difference of their cubes is 9728 .Find thenumbers explain with clear steps

Answer 1

let number be 2x and 3x such that their ratio is 2:3

(3x)∧3-(2x)∧3=9728
27x∧3-8x∧3=9728
19x∧3=9728
x∧3=512
x=8
2*8= 16 and  3*8 =24

Numbers are 16 an 24

Answer 2

Answer:

16,24

Step-by-step explanation:

Given:

Ratio of the two numbers is 2:3

To find:

The unknown numbers

Solution:

One of the key ideas in mathematics is ratio and proportion. The ratio concept is used to compare two quantities, but the proportion concept is used to demonstrate equality between two ratios.

The formula for calculating the ratio of two numbers, a and b, is a divided by b, written as a/b or a:b.

While the proportion is denoted as a:b::c:d or a/b=c/d, the relationship between the two ratios of a/b and c/d is.

Any two quantities can be compared using the ratio. The symbols a/b or a:b stand for the ratio of two numbers, a and b. Additionally, two or more such ratios will be deemed to be in proportion when they reach an equality. All ratio and proportion concepts are based on fractions. Some of the fundamental ideas in mathematics include the ratio and the proportion.

Let the numbers be 2x and 3x

Difference of their cubes = 9728

According tot the question,

$3x^{3} -2x^{3} =9728\\27x^{3}-8x^{3}=9728\\19x^{3}=9728\\x^{3}=512\\x=8$

Thus the numbers are ,

$2x=(2)(8)=16\\3x=(3)(8)=24$

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