If 152 is divided into four parts proportional to 3, 4, 5 and 7, then the smallest part is
24
To solve the problem of dividing 152 into four parts proportional to 3, 4, 5, and 7, we need to use the concept of ratios.
The given ratios are 3, 4, 5, and 7. Let's assume these parts are represented by \(3x\), \(4x\), \(5x\), and \(7x\) respectively.
The sum of these parts equals the total, which is 152. Therefore, we can write the equation:
\(3x + 4x + 5x + 7x = 152\)
\((3 + 4 + 5 + 7)x = 152\)
\(19x = 152\)
Solving for \(x\), we get:
\(x = \frac{152}{19}\)
Upon simplifying, \(x = 8\).
Now, we can find the parts:
- First part: \(3x = 3 \times 8 = 24\)
- Second part: \(4x = 4 \times 8 = 32\)
- Third part: \(5x = 5 \times 8 = 40\)
- Fourth part: \(7x = 7 \times 8 = 56\)
Therefore, the smallest part is 24.
This matches the provided option 24, which is the correct answer.
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