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¿cuales números naturales de dos cifras cumplen la condición de que su triple disminuido en 5, sea menor que su doble aumentado en 8?

User Mikrasya
by
7.3k points

1 Answer

4 votes

Answer: 10, 11 and 12.

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.

User JayK
by
8.2k points
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