Answer: 10, 11 and 12.
Step-by-step explanation:
This translates to:
Find the natural numbers of two digits that fulfill the condition that when triple and decreased in 5, is less than the double increased in 8?
suppose that A is our number of two digits, this means that:
3*A - 5 < 2*A + 8
It makes sense to start with the smaller number of two digits, 10.
3*10 - 5 < 2*10 + 8
25 < 28
this is true.
Now let's check the next one, 11.
11*3 - 5 < 2*11 + 8
28 < 30
This is true again, now let's try with the next one, 12.
3*12 - 5 < 2*12 + 8
31 < 32
This is true again, now let's find the last one.
3*13 - 5 < 2*13 + 8
34 < 34
this is not true, so the numbers that fulfill the condition are 10, 11, and 12.
A faster way to prove it is, suppose that both sides of our inequality are equal, then find the value of A.
3*A - 5 = 2*A + 8
3*A - 2*A = 8 + 5 = 13
A = 13
This means that any number of two digits less than 13 fulfills the condition, those numbers are 10, 11, and 12.
