Solve for X: Finding the Unknown in Ratio 'X:60 = 5:12'

Q: Why can't I just add the numbers in the ratios?

Ratios show multiplication relationships, not addition! Think of it like recipes - if 2 cups flour makes 12 cookies, then 4 cups flour makes 24 cookies (doubled), not 14 cookies (added).

Q: What does X:60 = 5:12 actually mean?

It means X is to 60 in the same way that 5 is to 12. The relationship between X and 60 is identical to the relationship between 5 and 12.

Q: How do I remember which numbers to multiply together?

Think of an X pattern! In $ \frac{X}{60} = \frac{5}{12} $, multiply the diagonal pairs: X × 12 and 60 × 5. The X helps you remember to cross-multiply!

Q: How do I check if 25 is really correct?

Substitute back! Does $ \frac{25}{60} = \frac{5}{12} $? Simplify 25/60 by dividing both by 5 to get 5/12. Perfect match!

Ratio Proportions with Cross-Multiplication

The ratio between X and 60 is like the ratio between 5 and 12.
Calculate the value of X.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The ratio between X and 60 is like the ratio between 5 and 12.
Calculate the value of X.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Set up the proportion based on the given ratios.
Step 2: Apply cross-multiplication to solve for $X$ .
Step 3: Simplify and perform arithmetic calculations to find the value of $X$ .

Now, let's work through each step:

Step 1: The problem gives us the proportion $\frac{X}{60} = \frac{5}{12}$ .

Step 2: Using cross-multiplication, we have:

$X \times 12 = 5 \times 60$

Step 3: Simplify the equation:

$12X = 300$

To isolate $X$ , divide both sides by 12:

$X = \frac{300}{12}$

Perform the division:

$X = 25$

Therefore, the solution to the problem is $X = 25$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Proportion Rule: Set up equal ratios as fractions: X/60 = 5/12
Cross-Multiply: Multiply diagonally: X × 12 = 5 × 60 = 300
Verify: Check 25/60 = 5/12 by reducing both to 5/12 ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting across ratios instead of cross-multiplying
Don't try X + 60 = 5 + 12 or X - 60 = 5 - 12 = wrong operations! Ratios show multiplication relationships, not addition. Always cross-multiply: X × 12 = 5 × 60.

Practice Quiz

Test your knowledge with interactive questions

What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

Why can't I just add the numbers in the ratios?

Ratios show multiplication relationships, not addition! Think of it like recipes - if 2 cups flour makes 12 cookies, then 4 cups flour makes 24 cookies (doubled), not 14 cookies (added).

What does X:60 = 5:12 actually mean?

It means X is to 60 in the same way that 5 is to 12. The relationship between X and 60 is identical to the relationship between 5 and 12.

How do I remember which numbers to multiply together?

Think of an X pattern! In $\frac{X}{60} = \frac{5}{12}$ , multiply the diagonal pairs: X × 12 and 60 × 5. The X helps you remember to cross-multiply!

Can I solve this a different way?

Yes! You could find what number makes 5/12 equal to something over 60. Since $12 \times 5 = 60$ , multiply both parts of 5:12 by 5 to get 25:60.

How do I check if 25 is really correct?

Substitute back! Does $\frac{25}{60} = \frac{5}{12}$ ? Simplify 25/60 by dividing both by 5 to get 5/12. Perfect match!

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