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Chapter 4: Problem 6

A mass of \(176 \mathrm{~kg}\) is divided in the ratio 4:5:7. Calculate the mass of each portion.

Short Answer

Expert verified
Answer: The masses of the 3 portions are 44 kg, 55 kg, and 77 kg.

Step by step solution

01

Calculate the sum of the ratios

To find the sum of the ratio 4:5:7, we simply add the numbers 4, 5, and 7 together: \(4 + 5 + 7 = 16\).
02

Determine the mass of each portion

Now that we know the sum of the ratios (16), we can calculate the mass of each portion. We will multiply the total mass (176 kg) by each portion's ratio and divide by the sum of the ratios (16). Portion 1 (ratio 4): \(\frac{176 \times 4}{16} = \frac{704}{16} = 44 \mathrm{~kg}\) Portion 2 (ratio 5): \(\frac{176 \times 5}{16} = \frac{880}{16} = 55 \mathrm{~kg}\) Portion 3 (ratio 7): \(\frac{176 \times 7}{16} = \frac{1232}{16} = 77 \mathrm{~kg}\) So, the masses of the 3 portions are 44 kg, 55 kg, and 77 kg.

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