125 is 250% of what number? 4.) 45% of 70 is what number? 5.) What percent of 300 is 75?
The Correct Answer and Explanation is:
Let’s solve each question first, then provide a full 300-word explanation.
Solutions
- 125 is 250% of what number?
Let the unknown number be x.
250% of x = 125
→ 250100×x=125\frac{250}{100} \times x = 125100250×x=125
→ 2.5x=1252.5x = 1252.5x=125
→ x=1252.5=50x = \frac{125}{2.5} = 50x=2.5125=50
✅ Answer: 50
- 45% of 70 is what number?
→ 45100×70=31.5\frac{45}{100} \times 70 = 31.510045×70=31.5
✅ Answer: 31.5
- What percent of 300 is 75?
Let the unknown percent be x.
→ x100×300=75\frac{x}{100} \times 300 = 75100x×300=75
→ 3x=753x = 753x=75
→ x=753=25x = \frac{75}{3} = 25x=375=25
✅ Answer: 25%
Explanation
Understanding percentages is crucial in both everyday life and mathematics. A percentage represents a part per hundred. For instance, 50% means 50 out of 100, or half of something. Let’s break down each question using this concept.
In the first question, “125 is 250% of what number?” we are asked to reverse the process of finding a percentage. Instead of taking a percentage of a known number, we are given the result (125) and the percentage (250%) and asked to find the original number. Since 250% means 2.5 times a number, we divide 125 by 2.5 to find that the original number is 50.
In the second question, “45% of 70 is what number?” we apply a straightforward percentage calculation. 45% is 0.45 in decimal form. Multiplying 0.45 by 70 gives us the part of 70 that represents 45%, which is 31.5.
The third question, “What percent of 300 is 75?” requires converting a ratio into a percentage. This involves dividing 75 by 300 to find what portion of 300 it is. 75300=0.25\frac{75}{300} = 0.2530075=0.25, and multiplying by 100 converts this to a percentage: 25%.
In summary, solving percentage problems involves understanding the basic relationship between the part, the whole, and the percent. Using simple algebra or proportional reasoning helps find unknowns efficiently. Whether calculating discounts, interest, or data analysis, mastering percentages is a valuable skill.
