Valuable percentages
Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?
These numbers have been written as percentages. Can you work out which has the greatest value?
Age
11 to 14
Challenge level
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