Question

how can percents show proportional relationships between quantities and be used to solve problems?

Explanation:

Percents represent a part - whole relationship. For example, if \(x\) is \(p\%\) of \(y\), we can write the equation \(\frac{x}{y}=\frac{p}{100}\). This proportion can be used to solve problems. Say we know \(p = 20\) and \(y=100\), then from \(\frac{x}{100}=\frac{20}{100}\), we find \(x = 20\). If we know \(x = 15\) and \(p=30\), then \(\frac{15}{y}=\frac{30}{100}\), cross - multiplying gives \(30y=15\times100\), so \(y = 50\).

Answer:

Percents show proportional relationships as \(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\). This proportion can be used to solve problems by cross - multiplying and isolating the unknown variable.