If 7:x=17.5:22.5 , then find the value of x .

The correct answer is Option (2) → 9

Two equal ratios form a proportion. In \(a:b=c:d\), \(a\) and \(d\) are called the extremes and \(b\) and \(c\) the means, and the product of the extremes equals the product of the means, so the two ratios can be written as equal fractions and cross-multiplied.

• The proportion as fractions: \(\displaystyle \frac{7}{x}=\frac{17.5}{22.5}\)

• Cross-multiplying: \(17.5x=7\times22.5=157.5\)

• Value of \(x\): \(\displaystyle x=\frac{157.5}{17.5}=9\)