42 Is 8 of What Number? Solve the Percent Equation
42 is 8% of 525. To find it, translate “42 is 8 of what number” into the equation 42 = 0.08 × x, then divide 42 by 0.08. The word “is” becomes the equals sign, and “of” signals multiplication.
Set Up the Percent Equation
A percent is a number out of 100, so 8% means 8 ÷ 100 = 0.08. When a percent problem says “of,” it means multiply, and “what number” is the unknown we call x.
That gives us:
42 = 0.08 × x
Here, 42 is the part, 0.08 is the rate (8% as a decimal), and x is the whole — the number we’re solving for. This is the standard percent equation: part = rate × whole.
Quick example of the setup in another case: if you were told “15 is 5% of what number,” you’d write 15 = 0.05 × x. Same structure, different values.
Solve and Verify the Answer
To isolate x, divide both sides by 0.08:
x = 42 ÷ 0.08 = 525
So the whole is 525.
Check the work by finding 8% of 525:
- 0.08 × 525 = 42
Because 8% of 525 equals 42, the answer is confirmed. You can also sanity-check the logic: 8% is a small share, so the whole should be much larger than the part. Since 525 is far bigger than 42, the result is reasonable.
This same method works for any “part is some percent of what number” question — convert the percent to a decimal, set part = decimal × whole, and divide.
Key Takeaways
- The equation for “42 is 8% of what number” is 42 = 0.08 × x.
- Solve by dividing the part by the decimal rate: 42 ÷ 0.08 = 525.
- Verify by multiplying: 0.08 × 525 = 42.
- General rule: whole = part ÷ (percent as a decimal).
