Answer :
the smallest possible value of the larger integer is z = 9.
what is the smallest possible value of the larger integer?
Let's define the 3 positive integers, from lowest to largest, as:
x, y, and z.
We know that:
x + y + z = 20
And the difference between the two smaller integers is:
y - x = 5
Then we can write:
y = x + 5
Replacing that, we can write:
x + (x + 5) + z = 20
2x + z = 20 - 5
2x + z = 15
If we isolate z, we get:
z = 15 - 2x
Now, our numbers are positive integers, so, if we take x = 1, then:
z = 15 - 2*1 = 13
y = 1 + 5 = 6
Now, we want to get the minimum value of z, then we need to maximize x.
The maximum value of x that we can take (such that x < y < z) is:
x = 3
Then:
z = 15 - 2*3 = 9
y = 3 + 5 = 8
This means that the smallest possible value of the larger integer is z = 9.
If you want to learn more about integer numbers:
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