Write and solve a proportion to answer the question. 75% of 124 is what number a ? Write and solve a proportion to answer the question. 72 is what percent of 45?
The correct answer and explanation is:
Let’s solve both proportion problems step by step.
🔹 1. 75% of 124 is what number (a)?
We can write this as a proportion: 75100=a124\frac{75}{100} = \frac{a}{124}
Now, solve the proportion using cross-multiplication: 75×124=100×a75 \times 124 = 100 \times a 9300=100a9300 = 100a a=9300100=93a = \frac{9300}{100} = 93
✅ Answer: 75% of 124 is 93
🔹 2. 72 is what percent of 45?
Let’s call the unknown percent x. The proportion becomes: x100=7245\frac{x}{100} = \frac{72}{45}
Now, solve by cross-multiplying: x×45=72×100x \times 45 = 72 \times 100 45x=720045x = 7200 x=720045=160x = \frac{7200}{45} = 160
✅ Answer: 72 is 160% of 45
📘 Explanation (300 words)
Proportions are powerful tools in solving percentage problems. A proportion is an equation stating that two ratios are equal. Percentage problems typically involve three quantities: the part, the whole, and the percent. By organizing these into a proportion, we can solve for any one of the unknowns.
Problem 1: When the question asks, “75% of 124 is what number?”, we know the percent (75%) and the whole (124), and we’re solving for the part (which we called a). We express this as a ratio of percent over 100 set equal to the unknown part over the whole: 75100=a124\frac{75}{100} = \frac{a}{124}
Solving gives us a = 93, which means 75% of 124 is 93.
Problem 2: When the question asks, “72 is what percent of 45?”, we are given the part (72) and the whole (45) and need to find the percent. Again, we set up a proportion: x100=7245\frac{x}{100} = \frac{72}{45}
Solving this gives us x = 160, meaning 72 is 160% of 45.
This tells us that 72 is not just 100% of 45, but 60% more—it’s more than the whole.
Proportions like these help visualize and solve percentage problems in a structured and reliable way.