Question

The sum of five different positive integers is 100. If the smallest of these integers is 10, what is the larges possible value of one of the other four integers?

Answer 1

The smallest integer is 10. So the other four numbers add to 100 - 10 = 90

Answer 2

Is it that simple???

Answer 3

If x, y, z and w are the four numbers, then

x+y+z+w = 90

Answer 4

Now make x as large as possible

Answer 5

the answer isn't 90, but it helps get you the answer

Answer 6

How do you find it when you don't even know one of the letters?

Answer 7

Let's make x as large as possible

Answer 8

Can x = 90?

Answer 9

Yes, right?

Answer 10

but that would make y, z, and w all be 0

Answer 11

x+y+z+w = 90

90+0+0+0 = 90

Answer 12

So 84?

Answer 13

good,

x+y+z+w = 90

84 + 1 + 2 + 3 = 90

Answer 14

anything larger for x would make y, z, or w have to become smaller (and either not be positive, or not be different)

Answer 15

Thank you!! I appreciate it a lot

Answer 16

you're welcome