Solve the Ratio Equation: Finding X in 20:4x=5

Ratio Equations with Variable Denominators

Solve the equation

20:4x=5 20:4x=5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's write division as a fraction
00:06 Multiply by denominator to eliminate the fraction
00:19 Simplify what we can
00:25 Isolate the unknown X, and calculate
00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the equation

20:4x=5 20:4x=5

2

Step-by-step solution

To solve the exercise, we first rewrite the entire division as a fraction:

204x=5 \frac{20}{4x}=5

Actually, we didn't have to do this step, but it's more convenient for the rest of the process.

To get rid of the fraction, we multiply both sides of the equation by the denominator, 4X.

20=5*4X

20=20X

Now we can reduce both sides of the equation by 20 and we will arrive at the result of:

X=1

3

Final Answer

x=1 x=1

Key Points to Remember

Essential concepts to master this topic
  • Ratio Rule: Convert ratio notation to fraction form for easier solving
  • Technique: Multiply both sides by denominator: 4x×5=20x 4x \times 5 = 20x
  • Check: Substitute x=1 back into original ratio: 20:4(1) = 20:4 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Treating the colon as subtraction instead of division
    Don't interpret 20:4x as 20-4x = completely wrong operation! The colon means division, not subtraction, leading to entirely incorrect equations. Always remember that a:b means a÷b or a/b.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( 3x=18 \)

FAQ

Everything you need to know about this question

What does the colon symbol mean in math?

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The colon : means division or "ratio of". So 20:4x is the same as 204x \frac{20}{4x} or 20÷(4x).

Why do we multiply both sides by 4x?

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Multiplying by the denominator eliminates the fraction! This turns 204x=5 \frac{20}{4x} = 5 into the simpler equation 20 = 20x.

Can I solve this without converting to a fraction?

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Yes! You can think of it as "20 divided by 4x equals 5", so 20 = 5 × 4x. Both methods give the same answer.

How do I check if x=1 is correct?

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Substitute back: 20:4(1) = 20:4 = 5. Since 20÷4 = 5, our answer is correct!

What if I got a different answer like x=5?

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Always verify by substituting back! If x=5, then 20:4(5) = 20:20 = 1, not 5. This shows x=5 is incorrect.

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