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QuestionMathematics
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What x-value makes the set of ratios equivalent?
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Answer
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Step 1:: Identify the given ratios and their corresponding quantities.
The given ratios are:
Step 2:\frac{1}{4} : 1 foot
2. $$\frac{1}{2}$$ : 1 foot
Step 3:\frac{3}{4} : 1 foot
4. $$\frac{x}{1}$$ : 1 foot
Step 4:: Set up an equation to find the value of x that makes the sets of ratios equivalent.
\frac{1}{1} = \frac{1 \times 1}{4 \times x} = \frac{1}{4x}
For the sets of ratios to be equivalent, the ratio of the quantities must be the same for each pair of corresponding ratios. In other words, the product of the first ratio and the quantity of the fourth ratio should be equal to the product of any other pair of corresponding ratio and quantity. Let's test this by multiplying the first ratio by 4 to make the quantities equal: So, we need to find the value of x that satisfies the following equation:
Step 5:: Solve for x.
x = \frac{1}{4}
To solve for x, cross-multiply and divide:
Final Answer
The value of x that makes the set of ratios equivalent is \frac{1}{4}.
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