60% of what number is 24? a/w = p/100 24/w = 60/100 24 * 100 = 60 * w 2400 / 60 = 60w / 60 w = 40 Am I correct?
The Correct Answer and Explanation is:
Yes, the answer is correct. The number is 40. Here’s a detailed explanation of how the solution works:
To find what number gives 24 when 60% of it is taken, the relationship between the part and the whole can be expressed using the formula: aw=p100\frac{a}{w} = \frac{p}{100}wa=100p
Where:
- aaa is the part (24),
- www is the unknown whole number,
- ppp is the percentage (60).
Substitute the known values: 24w=60100\frac{24}{w} = \frac{60}{100}w24=10060
To eliminate the denominators, cross-multiply: 24×100=60×w24 \times 100 = 60 \times w24×100=60×w 2400=60w2400 = 60w2400=60w
Solve for www by dividing both sides by 60: 240060=w\frac{2400}{60} = w602400=w w=40w = 40w=40
This confirms that 60% of 40 is 24. To check, multiply 40 by 60%, which means: 40×0.60=2440 \times 0.60 = 2440×0.60=24
This verifies the accuracy of the calculation.
This type of problem belongs to the category of percentage problems involving finding the base or whole when given the percentage and the result. The technique involves converting the percentage to a fraction or decimal, setting up a proportion, and solving for the unknown variable using basic algebraic manipulation. Cross-multiplication simplifies the fraction equation into a solvable linear equation. This method is reliable and works for any similar percentage problem.
