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Is your relationship worth repairing? Get "Build Before You Promise" → Relationship Repair When Love Is Still There but the Relationship Is Falling Apart Sometimes the relationship does not need another argument. It needs two people willing to stop defending themselves long enough to understand what is actually breaking. By Edwin Ogie • Author of The Relationship Repair Handbook , Build Before You Promise , Emotional Mastery , and The Value of You Not every broken relationship is a relationship without love. Sometimes two people still love each other deeply, but they have become exhausted by unresolved arguments, poor communication, resentment, disappointment and repeated misunderstandings. They may still care. They may still want the relationship. They may e...
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Variation (Direct, Inverse, Joint, Partial & Percentage Changes)

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EO

Variation — Edwin Ogie Library

Direct, inverse, joint, partial variations & percentage changes — worked examples and CBT for students.

Keywords: variation, proportionality Edwin Ogie Library

Introduction to Variation

Variation describes how one quantity changes with another. We study direct, inverse, joint, partial variations and percentage increases/decreases to solve many real-world and exam problems.

Quick links: Edwin Ogie Library (home) • Jump to CBT Quiz

Direct Variation

If y varies directly as x then y ∝ x or y = kx, where k is constant of proportionality.

Example

Q: y = 20 when x = 4. Find y when x = 10.

Inverse Variation

If y varies inversely as x: y ∝ 1/x or y = k / x.

Example

Q: y = 3 when x = 8. Find y when x = 16.

Joint & Partial Variation

Joint:

If y varies jointly as x and z: y = k x z.

Partial:

Partial/combined: y = k x + c (kx varies, c is constant).

Example (Joint)

Q: z = 30 when x=2 and y=5; find z when x=3 and y=4 (assuming z = kxy).

Percentage Increase & Decrease

Increase = [(New − Old)/Old] × 100%

Decrease = [(Old − New)/Old] × 100%

Example

Q: 80 → 100: percentage increase?

10 Worked Examples (Solutions Hidden)

Example 1 — Direct Variation

Q: If y varies directly as x and y=20 when x=4, find y when x=10.

Example 2 — Inverse Variation

Q: y=3 when x=8; find y when x=16.

Example 3 — Joint Variation

Q: z=30 when x=2, y=5; find z when x=3, y=4.

Example 4 — Partial Variation

Q: If y = 2x + 5, find y when x = 7.

Example 5 — Percentage Increase

Q: 80 → 100: % increase?

Example 6 — Percentage Decrease

Q: 120 → 90: % decrease?

Example 7 — Direct Variation % Change

Q: If x increases 20% in y = kx, what % does y increase?

Example 8 — Inverse Variation % Change

Q: y = k/x; x increases 50% → % change in y?

Example 9 — Joint Variation with change

Q: z=48 when x=4,y=3. If x+25% and y−20%, what's z?

Example 10 — Partial Variation & %

Q: y = 3x + 10; x increases 10% — approximate % change in y?

Summary

  • Direct: y = kx
  • Inverse: y = k / x
  • Joint: y = k x z (or more variables)
  • Partial: y = kx + c
  • Percentage change: Use original value as base.

30-Question CBT Quiz (15 minutes)

Designed for JSS to early senior students. Click Start Quiz to begin.

Time Remaining: 15:00
Resources: Edwin Ogie Library.
Edwin Ogie Library — learn, practice, and prepare.

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