Two elements X and Y combine to form compounds A, B, and C. The ratio of different masses of Y which combine with a fixed mass of X in A, B, and C is 1:3:5. If 32 parts by mass of... Two elements X and Y combine to form compounds A, B, and C. The ratio of different masses of Y which combine with a fixed mass of X in A, B, and C is 1:3:5. If 32 parts by mass of X combines with 84 parts by mass of Y in B, then in C, 16 parts by mass of X will combine with how many parts by mass of Y?
Understand the Problem
The question is presenting a problem involving two elements, X and Y, that combine in fixed ratios to form different compounds. It seeks to determine how many parts by mass of Y will combine with a certain mass of X based on given ratios and combinations.
Answer
The number of parts by mass of Y that will combine with 16 parts by mass of X is $42$.
Answer for screen readers
The answer is $42$ parts by mass of Y.
Steps to Solve
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Identify the given ratios The problem states that the ratios of Y that combine with a fixed mass of X in compounds A, B, and C are 1:1, 3:1, and 16:X respectively.
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Set up the equations based on the ratios Based on the information:
- In compound A: For every 1 part of X, Y = 1 part of Y
- In compound B: For every 3 parts of X, Y = 84 parts of Y (given)
- For compound C: For every 16 parts of X, we need to find parts of Y based on parts of X.
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Use the provided information to find the mass of Y for compound C From the provided data, if 32 parts of X combine with 84 parts of Y, it can be set as: $$ \text{Ratio of X to Y in B} = \frac{32}{84} $$
To find Y needed for C when $16$ parts of X are used: $$ \frac{16}{x} = \frac{32}{84} $$
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Cross multiply and solve for x Cross-multiplying the equation gives: $$ 32x = 16 \times 84 $$
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Calculate x Now, calculate $x$: $$ x = \frac{16 \times 84}{32} $$ Simplify the values: $$ x = \frac{1344}{32} = 42 $$
The answer is $42$ parts by mass of Y.
More Information
The mass of Y is calculated based on the ratios given in the problem. This solution follows consistent ratios of elements that combine to form compounds.
Tips
- A common mistake is misinterpreting the ratios and applying them incorrectly in a cross-multiplication step.
- Another mistake could be not simplifying the fractions before calculating, which can lead to incorrect results.
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