Assume that neither x nor y is equal to 0, to permit division by x and by y.
`2x:y` is equivalent to `4x:8,500`. What is y?

Answer

To solve the problem, we need to find the value of \( y \) given that the ratios \( 2x:y \) and \( 4x:8500 \) are equivalent.

### Step-by-step Solution:

1. **Set up the ratio equation**:
Since the ratios \( 2x:y \) and \( 4x:8500 \) are equivalent, we can express this as:
\[ \frac{2x}{y} = \frac{4x}{8500} \]

2. **Cross-multiply to eliminate the fractions**:
To solve for \( y \), we can cross-multiply:
\[ 2x \cdot 8500 = 4x \cdot y \]

3. **Simplify the equation**:
This simplifies to:
\[ 17000x = 4xy \]

4. **Isolate \( y \)**:
Now, we can isolate \( y \) by dividing both sides by \( 4x \) (noting that \( x \neq 0 \)):
\[ y = \frac{17000x}{4x} \]

5. **Cancel \( x \)**:
Since \( x \) is not equal to zero, we can cancel \( x \) from the numerator and denominator:
\[ y = \frac{17000}{4} \]

6. **Perform the division**:
Now, calculate \( \frac{17000}{4} \):
\[ y = 4250 \]

### Final Answer:
Thus, the value of \( y \) is \( 4250 \).

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