If x / y = 3/7 and 21x + 6y = 315 find the value of y.?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The problem provides two equations: a ratio (x/y = 3/7) and a linear equation (21x + 6y = 315).
The most direct method is substitution. First, rearrange the ratio equation to express x in terms of y: x = (3/7)y.
Substitute this expression for x into the second equation: 21((3/7)y) + 6y = 315.
Simplify the equation: 9y + 6y = 315, which becomes 15y = 315.
Solving for y by dividing 315 by 15 gives the final answer, y = 21.

Option A: This value is incorrect. It may arise from a miscalculation in the final division step (315 / 15).
Option C: This value is incorrect. It may be the result of an arithmetic error during the simplification of the equation.
Option D: This value is incorrect. It might be chosen if one incorrectly calculates 315 / 15, perhaps by rounding down or making a division error.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a system of linear equations with two variables using the substitution method as background academic context rather than a clinical decision trigger.
This question tests fundamental mathematical and problem-solving skills, which are essential for various calculations in nursing practice.
Accurate calculation is critical for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data, where a small error can have significant consequences.
What if the ratio was x/y = 7/3? The value of x would be (7/3)y. Substituting this into the second equation would give 21((7/3)y) + 6y = 315, leading to 49y + 6y = 315, or 55y = 315, resulting in a different value for y.

How to Approach the Question

First, carefully read the question and identify the two given mathematical equations.
Recognize that you have a system of two equations with two unknowns (x and y).
Look for the easiest way to relate the two equations. The ratio x/y = 3/7 provides a simple way to express one variable in terms of the other (x = 3y/7).
Substitute this expression into the second equation (21x + 6y = 315). This will create a new equation with only one variable (y).
Solve the resulting single-variable equation for 'y' through algebraic simplification.
Double-check your arithmetic, especially the final division, to ensure accuracy before selecting your answer.

Concept Tested & Keywords

Concept Tested: Solving a system of linear equations with two variables using the substitution method.
Stem keywords: x / y = 3/7, 21x + 6y = 315, value of y
Lead-in keywords: find the value

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Practise the full DSSSB - 28 August 2019 (Shift-1)

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