To determine if the ratios \( 86:94 \) and \( 76:54 \) are equivalent, we can simplify both ratios and compare them.
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Simplifying the first ratio \( 86:94 \):
- Find the greatest common divisor (GCD) of 86 and 94.
- The GCD of 86 and 94 is 2.
- Divide both numbers by their GCD: \[ \frac{86}{2} = 43, \quad \frac{94}{2} = 47 \]
- Therefore, \( 86:94 = 43:47 \).
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Simplifying the second ratio \( 76:54 \):
- Find the GCD of 76 and 54.
- The GCD of 76 and 54 is 2.
- Divide both numbers by their GCD: \[ \frac{76}{2} = 38, \quad \frac{54}{2} = 27 \]
- Therefore, \( 76:54 = 38:27 \).
Now, we can compare the simplified ratios \( 43:47 \) and \( 38:27 \).
- To check if \( 43:47 \) and \( 38:27 \) are equivalent, we can cross-multiply:
- \( 43 \times 27 = 1161 \)
- \( 38 \times 47 = 1786 \)
Since \( 1161 \neq 1786 \), the ratios \( 86:94 \) and \( 76:54 \) are not equivalent.