Question

THE SUM OF TWO CONSTRUCTIVE INTEGERS IS NO MORE THAN 209.

WHAT IS THE LARGER OF THE TWO INTEGERS?


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Answer 1

x = first integer

x+1 = integer right after x

For example, if x = 10, then the next one after that is x+1 = 10+1 = 11. So 10 and 11 are consecutive integers (one follows right after the other)

The sum of those two integers x and x+1 add to x+x+1 = 2x+1

This sum is no more than 209, therefore,

`2x+1 \le 209`

`2x+1-1 \le 209-1`

`2x \le 208`

`(2x)/(2) \le (208)/(2)`

`x \le 104`

Therefore the largest x can be is 104

If x = 104, then x+1 = 104+1 = 105

Final Answer: 105

Note how 104+105 = 209, which helps confirm the answer