Alloy

The first alloy is a mixture of two metals in the ratio 1:2; the second is a mixture of the same metals in the ratio 2:3. At what ratio do we have these two alloys put into the furnace to obtain a new metal alloy with a ratio of 17:27? (All three ratios correspond to the same order of the two metals).

Correct answer:

r = 9:35

Step-by-step explanation:

k_{1} = \frac{1}{1 + 2} \cdot m_{1} + \frac{2}{2 + 3} \cdot m_{2} k_{2} = \frac{2}{1 + 2} \cdot m_{1} + \frac{3}{2 + 3} \cdot m_{2} k_{1} = \frac{1}{3} \cdot m_{1} + \frac{2}{5} \cdot m_{2} k_{2} = \frac{2}{3} \cdot m_{1} + \frac{3}{5} \cdot m_{2} k_{1} / k_{2} = 17 : 27 r = m_{1} / m_{2} 17 / 27 = \frac{\frac{1}{3} \cdot m _{1} + \frac{2}{5} \cdot m _{2}}{\frac{2}{3} \cdot m _{1} + \frac{3}{5} \cdot m _{2}} 17 \cdot (\frac{2}{3} \cdot m_{1} + \frac{3}{5} \cdot m_{2}) = 27 \cdot (\frac{1}{3} \cdot m_{1} + \frac{2}{5} \cdot m_{2}) 17 \cdot (\frac{2}{3} \cdot r + \frac{3}{5}) = 27 \cdot (\frac{1}{3} \cdot r + \frac{2}{5}) r = \frac{2 7 \cdot \frac{2}{5} - 1 7 \cdot \frac{3}{5}}{1 7 \cdot \frac{2}{3} - 2 7 \cdot \frac{1}{3}} = \frac{9}{3 5} ≐ 0.2571 Verifying Solution: m_{1} = 9 kg m_{2} = m_{1} / r = 9 / \frac{9}{3 5} = 9 : \frac{9}{3 5} = 9 \cdot \frac{3 5}{9} = \frac{9 \cdot 3 5}{9} = \frac{3 1 5}{9} = 35 kg k_{1} = \frac{1}{3} \cdot m_{1} + \frac{2}{5} \cdot m_{2} = \frac{1}{3} \cdot 9 + \frac{2}{5} \cdot 35 = 17 kg k_{2} = \frac{2}{3} \cdot m_{1} + \frac{3}{5} \cdot m_{2} = \frac{2}{3} \cdot 9 + \frac{3}{5} \cdot 35 = 27 kg t_{2} = k_{1} / k_{2} = 17 / 27 = \frac{1 7}{2 7} ≐ 0.6296

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
Check out our ratio calculator.
Do you have a system of equations and are looking for calculator system of linear equations?