Age Relationship Problem: Solve for Hector's Age Using 3x and -10 Relations

Luciana's age is 3 times Ivana's age.

Hector is 10 years younger than Luciana.

The sum of the three ages is 32.

How old is Hector?

To solve this problem, let's define the variables and set up the equation:

• Let Ivana's age be $x$.
• Then, Luciana's age is $3x$, since her age is three times Ivana's age.
• Hector, being 10 years younger than Luciana, would be $3x - 10$.

We know the sum of their ages is 32, so we set up the equation:

$x + 3x + (3x - 10) = 32$

Simplify the equation:

$x + 3x + 3x - 10 = 32$

$7x - 10 = 32$

Next, solve for $x$:

Add 10 to both sides:

$7x = 42$

Divide both sides by 7:

$x = 6$

Now that we know Ivana is 6 years old, we can find Hector's age:

Hector's age = $3x - 10 = 3(6) - 10 = 18 - 10 = 8$

Therefore, Hector is 8 years old.