Three whole numbers are each rounded to the nearest 10. The sun of the three rounded numbers is 80. What is the maximum possible sum of the original three numbers?

Question

Three whole numbers are each rounded to the nearest 10. The sum of the three rounded numbers is 80. What is the maximum possible sum of the original three numbers?

Answer 1

The answer is 92.

Let’s see what multiples of 10 add up to 80:

10+10+60, 10+20+50, 10+30+40, 20+20+40, 20+30+30.

Imagine the numbers had all been rounded up:

9+9+59=77, which is less than 80.

But if each number is rounded down to the nearest 10 the maximum ones digit is 4 for each of them, and 3 times 4 is 12, added to 80 is 92:

14+14+64=

14+24+54=

14+34+44=

24+24+44=

24+34+34=92.