45:60. 90:120 80:120. 60: 90

To find the missing value in the ratio 60:x, we can set up a proportion based on the ratios you provided: The ratios given are: - \( \frac{45}{60} \) - \( \frac{90}{120} \) - \( \frac{80}{120} \) All these ratios are equivalent. Let's simplify each one to see the common ratio. 1. \( \frac{45}{60} = \frac{3}{4} \) (simplifying by dividing numerator and denominator by 15) 2. \( \frac{90}{120} = \frac{3}{4} \) (simplifying by dividing by 30) 3. \( \frac{80}{120} = \frac{2}{3} \) (not equivalent, but let's use it for the context of finding a different missing value) Next, let's check the final ratio, which is \( \frac{60}{x} \). If we take \( \frac{60}{90} \), we can see if it matches with the above ratios. To find the \(x\): \[ \frac{60}{90} = \frac{2}{3} \] We can cross-multiply to solve: \[ 60 \cdot 3 = x \cdot 2 \] \[ 180 = 2x \] \[ x = 90 \] Thus, \(60 : 90\). So, the x in the ratio \(60 : x\) is \(90\).