Luis is 10 years older than his brother. Next year, he will be three times as old as his brother. If the brother's age is represented by a, what is Luis' age? What will be the brother's age next year?
Luis = a + 10
Luis + 1 = 3a
Substitute a+10 for a in second equation and solve for a. Insert that value into the first equation and solve for Luis. Check by inserting both values into the second equation.
Let's solve this step-by-step.
1. Let's assume the brother's age is represented by 'a'.
2. According to the given information, Luis is 10 years older than his brother, so Luis' age would be 'a + 10'.
3. Next year, Luis will be three times as old as his brother, which can be represented as 'a + 1 = 3(a + 1)'.
4. Solving the equation from step 3, we have 'a + 1 = 3a + 3'.
5. Simplifying, we get '2a = -2'.
6. Dividing both sides by 2, we get 'a = -1'.
7. Since age cannot be negative, we discard this solution.
8. Therefore, there is no valid age for the brother that satisfies the given conditions.
Hence, the problem statement seems to be inconsistent or may have been incorrectly stated.
To solve this problem, we can set up a system of equations based on the given information.
Let's represent Luis' age as L and the brother's age as a.
According to the problem, Luis is 10 years older than his brother, so we can write:
L = a + 10 Equation 1
Next year, Luis will be three times as old as his brother, so we can write:
L + 1 = 3(a + 1) Equation 2
Now, we can solve this system of equations to find the values of L and a.
We can start by substituting the value of L from Equation 1 into Equation 2:
(a + 10) + 1 = 3(a + 1)
Simplify the equation:
a + 11 = 3a + 3
Subtract a from both sides:
11 = 2a + 3
Subtract 3 from both sides:
8 = 2a
Divide both sides by 2:
a = 4
So, the brother's current age is 4.
Now, we can substitute this value back into Equation 1 to find Luis' current age:
L = 4 + 10
L = 14
Therefore, Luis' current age is 14.
To find the brother's age next year, we can add 1 to the current age:
Next year's age = 4 + 1
Next year's age = 5
Therefore, the brother's age next year will be 5.