Open Middle®
Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create an accurate number line.
Hint
What numbers can we fill in for 100% that will result in a single digit value for 30%?
What has to be true about the 100% value in order for the 75% value to result in a whole number?
What has to be true about the 100% value in order for the 75% value to result in a whole number?
Answer
6, 15, 20
Source: Adrianne Burns
6, 15, 20 is my answer.
How did you arrive at 615 20 do you have an explanation so I can explain it to myself and then teach my grandson how to do it correctly. Thanks
The number at 100 % has to be a whole number, but 30 % = 3/10 of that number and 75 % = 3/4 of that number also have to be whole numbers. So the number at 100 % has to be divisible by both 10 and 4. The smallest integer that is divisible by both 10 and 4 is 20. The next one would be 40, but 30 % of 40 would be 12, which is not a one-digit-number anymore.
I think that it is 6 15 20
6, 15, 20 is the only possible answer.
Are decimals not accepted?
This was very fun. I am going to pose the hint questions as a writing task at the end of the activity. I would also like to extend the problem to allow for decimals (while only use each digit up to one time) once the students solve the initial problem.