Question
The product of two positive numbers is 3645. If the first number is five times the second number, then the sum of the two numbers is:
The correct answer is
162
To solve this problem, we will follow these steps:
- Let's denote the second number as x. According to the problem, the first number is five times the second number. Therefore, the first number can be represented as 5x.
- The product of these two numbers is given as 3645. Therefore, we can write the equation as:
x \times 5x = 3645 - Simplify the equation:
5x^2 = 3645 - Divide both sides of the equation by 5 to solve for x^2:
x^2 = \frac{3645}{5} - Calculate the division:
x^2 = 729 - Take the square root of both sides to find x:
x = \sqrt{729} = 27 - Since the first number is five times the second number, the first number is:
5 \times 27 = 135 - Now, find the sum of the two numbers:
27 + 135 = 162
Therefore, the sum of the two numbers is 162, which matches the correct answer.
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Important Questions from Algebric Equations
- For what value of K is the equation \(\frac{0.009}{K} = 0.1\) true?
- Arnab buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 4 oranges and 3 bananas?
- Find the value of x satisfying: $5(5x^2 - 5) - 5(5x^2 + 7x - 2) = 14$
- The product of two positive numbers is 80. If the first number is five times of the second number, then the sum of the two numbers is:
- Find the value of x satisfying: $3(2x^2 - 5) - 2(3x^2 + 4x - 8) = 20$
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