Answer: Option B
Let the two numbers be 2x and 3x (as their ratio is 2:3).
The sum of their cubes is given as 945, which can be expressed as:
(2x)^3 + (3x)^3 = 8x^3 + 27x^3 = 35x^3 = 945
Solving for x, we get:
x^3 = 27x = 3
Therefore, the two numbers are 2x = 6 and 3x = 9.
The difference of the numbers is then:
9 - 6 = 3
Hence, the answer is option B. 3.
Explanation:To solve the problem, we need to use the given information to form equations and then solve for the unknowns. Here, we are given the ratio of the two numbers as well as the sum of their cubes. We can use these to form equations and solve for the numbers.
We start by expressing the two numbers in terms of x, which is a common factor. We use the ratio given to us to set up the expression, and we get 2x and 3x. We then use the sum of their cubes to form an equation, which we solve to find the value of x.
Once we have the value of x, we can find the two numbers by substituting x into the expressions we formed earlier. We then find the difference of the numbers to get the final answer.
In summary, the key steps to solving this problem are:

• Express the two numbers in terms of x
• Use the sum of their cubes to form an equation and solve for x
• Substitute x to find the two numbers
• Find the difference of the numbers to get the answer

Formulas and definitions:

• Ratio: a comparison of two quantities that are measured in the same units. It is often expressed as a fraction, with the first quantity as the numerator and the second quantity as the denominator.
• Cube: the product of a number multiplied by itself three times. It is denoted by an exponent of 3, e.g. 2^3 = 2 x 2 x 2 = 8.
• Equation: a mathematical statement that asserts the equality of two expressions. It contains an equal sign and can be solved to find the value of the unknown variable.
• Substitution: the process of replacing one expression with another that is equal to it. It is often used to simplify expressions or to solve equations.

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