The product of two numbers is 18.75 if one number is three times the other number is
The Correct Answer and Explanation is:
Correct answer:
The other number is 2.5
Explanation
We are told that the product of two numbers is 18.75 and that one number is three times the other. To find the unknown numbers, we can use algebra.
Let us assume the smaller number is x.
Then, according to the problem, the larger number is 3x because it is three times the smaller one.
Now we multiply the two numbers:
x × 3x = 18.75
This simplifies to:
3x² = 18.75
Next, solve for x² by dividing both sides of the equation by 3:
x² = 18.75 ÷ 3
x² = 6.25
Now take the square root of both sides to find x:
x = √6.25
x = 2.5
So, the smaller number is 2.5.
Since the larger number is three times the smaller number:
3 × 2.5 = 7.5
Therefore, the two numbers are 2.5 and 7.5.
To double-check:
2.5 × 7.5 = 18.75
which matches the product given in the question.
This kind of problem is a classic example of how algebra helps us break down relationships between numbers. By setting up one variable and expressing the other in terms of that variable, we can convert a word problem into a solvable mathematical equation. In this case, using x to represent one number and 3x for the other allowed us to set up a quadratic equation. Once we solved that, we could find both values easily. This technique can be applied to many types of problems involving number relationships, such as age problems, ratio problems, or geometry.
