$\frac{5}{8}$ of $24 = \frac{15}{7}$ of?

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The problem is set up as an equation: (5/8) * 24 = (15/7) * x.
First, the left side of the equation is simplified: (5/8) * 24 = 5 * 3 = 15.
The equation becomes 15 = (15/7) * x.
To solve for x, both sides are multiplied by the reciprocal of 15/7, which is 7/15.
x = 15 * (7/15), which simplifies to x = 7.

Option A: This value (7/225) would result from a significant calculation error, possibly by incorrectly dividing 7 by 15 twice (7 / (15*15)).
Option C: The number 8 is the denominator of the fraction 5/8. It is a component of the problem but not the solution.
Option D: The number 15 is the result of the calculation on the left side of the equation (5/8 of 24). It is an intermediate step, not the final answer.

Visual 1: Flowchart - A flowchart illustrating the step-by-step process of solving the equation. It would show: 1. Set up the equation. 2. Simplify the left side. 3. Isolate the variable 'x'. 4. Calculate the final value.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving fractional equations as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and algebraic skills, which are fundamental for nurses.
Accurate calculation is critical in clinical practice for tasks such as medication dosage calculation, IV drip rate adjustment, and interpreting lab results.
What if the equation involved medication dosage, such as 'A patient needs 2/3 of a 750mg tablet. This is equal to 5/2 of what smaller dose tablet?' An error in this calculation could lead to a significant medication error, highlighting the importance of mathematical proficiency.

How to Approach the Question

First, identify that the question is asking you to find an unknown value in an equation involving fractions.
Translate the words into a mathematical equation. Let the unknown value be 'x'. The equation is (5/8) * 24 = (15/7) * x.
Solve one side of the equation first to simplify it. Here, calculate the value of (5/8) * 24.
Rearrange the simplified equation to solve for 'x'. This involves isolating 'x' on one side.
Perform the final calculation to find the value of 'x'.
Compare your result with the given options to find the correct answer.

Concept Tested & Keywords

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