Question
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Tutor-Verified Answer
Answer
The numbers 756 divided in the ratio \( 2:5:7 \) are 108, 270, and 378.
Solution
To divide 756 in the ratio \( 2:5:7 \), follow these steps:
1. **Understand the Ratio:**
- Let the three parts be \( 2x \), \( 5x \), and \( 7x \) respectively.
2. **Set Up the Equation:**
\[
2x + 5x + 7x = 756
\]
\[
14x = 756
\]
3. **Solve for \( x \):**
\[
x = \frac{756}{14} = 54
\]
4. **Find Each Part:**
- First part: \( 2x = 2 \times 54 = 108 \)
- Second part: \( 5x = 5 \times 54 = 270 \)
- Third part: \( 7x = 7 \times 54 = 378 \)
**Final Division:**
\[
756 \text{ divided in the ratio } 2:5:7 \text{ is } 108 : 270 : 378
\]
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Simplify this solution The Deep Dive
To divide 756 in the ratio \( 2:5:7 \), first, add the parts of the ratio together: \( 2 + 5 + 7 = 14 \). Next, determine the value of one part by dividing 756 by the total number of parts: \( \frac{756}{14} = 54 \). Now, multiply 54 by each part of the ratio: - For \( 2 \): \( 2 \times 54 = 108 \) - For \( 5 \): \( 5 \times 54 = 270 \) - For \( 7 \): \( 7 \times 54 = 378 \) Thus, the numbers are \( 108 \), \( 270 \), and \( 378 \). To verify, add them together: \( 108 + 270 + 378 = 756 \). Success!
