Valuable Percentages
Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?
Problem
Which of the following has the greatest value?
A) 50% of 10
B) 40% of 20
C) 30% of 30
D) 20% of 40
E) 10% of 50
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: the greatest is 30% of 30
Finding the values
50% of 10 = 10$\div$2 = 5
40% of 20 = 10$-$2 = 8
30% of 30 = 3$\times$3 = 9
20% of 40 = 4 + 4 = 8
10% of 50 = 50$\div$10 = 5
So 30% of 30 is the greatest
Using commutativity and strategy
$50\% \text{ of } 10 = \frac{50}{100}\times10 = \frac{10\times50}{100} = \frac{10}{100}\times50 = 10\%\text { of }50$
Similarly, $40\% \text{ of }20 = 20\%\text{ of }40$
So $30\%\text{ of }30$ is the only one without a partner - so it must be the greatest, because there is only one answer