A number is multiplied by three-fourths of itself to obtain 15,552. What is the number?

Appeared in: Haryana CHO - 2022

Explanation

The problem is translated into the algebraic equation: x * (3/4 * x) = 15,552, where x is the unknown number.
Simplifying the equation gives (3/4) * x² = 15,552.
To solve for x, first isolate x² by multiplying both sides by 4/3, which gives: x² = 15,552 * (4/3) = 20,736.
The final step is to find the square root of 20,736, which is 144.

Option A: If the number were 120, multiplying it by three-fourths of itself would result in 120 * (3/4 * 120) = 120 * 90 = 10,800, which does not equal 15,552.
Option B: If the number were 140, the calculation would be 140 * (3/4 * 140) = 140 * 105 = 14,700. This is not the required value of 15,552.
Option D: If the number were 154, the product would be 154 * (3/4 * 154) = 154 * 115.5 = 17,787. This is incorrect as the problem states the product is 15,552.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving an algebraic word problem involving fractions and square roots as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, a foundational skill for nurses.
Nurses use similar calculations daily for critical tasks such as determining medication dosages, calculating IV drip rates, and interpreting patient data, where accuracy is paramount for patient safety.
What if the question asked for a number multiplied by two-thirds of itself to obtain 15,552? The equation would change to x * (2/3 * x) = 15,552. This would lead to x² = 23,328, and the number would be approximately 152.7.

How to Approach the Question

First, carefully read the word problem to understand what is being asked. Identify the unknown value and represent it with a variable, such as 'x'.
Translate the words of the problem into a mathematical equation. 'A number is multiplied by three-fourths of itself' becomes 'x * (3/4 * x)'.
Set this expression equal to the given result: x * (3/4 * x) = 15,552.
Solve the resulting algebraic equation for the variable 'x'. This involves simplifying the expression and using inverse operations to isolate 'x'.
After finding a value for 'x', plug it back into the original word problem or equation to verify that it is the correct solution.

Concept Tested & Keywords

Concept Tested: Solving an algebraic word problem involving fractions and square roots.
Stem keywords: number, multiplied, three-fourths, 15,552
Lead-in keywords: What is

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E6 Nursing Fundamentals Taylor p. 920-922

Practise the full Haryana CHO - 2022

Attempt every question from this paper in a timed mock, then review the full solution for each one.