# Twice Albert's age plus Bob's age equals 75. In three years, Albert's age and Bob's age will add up to 64. How do you find their ages?

Jun 15, 2017

See a solution process below:

#### Explanation:

First, let's call Albert's age: $a$. And, let's call Bob's age: $b$

Now, we can write:

$2 a + b = 75$

$\left(a + 3\right) + \left(b + 3\right) = 64$ or $a + b + 6 = 64$

Step 1) Solve the first equation for $b$:

$- \textcolor{red}{2 a} + 2 a + b = - \textcolor{red}{2 a} + 75$

$0 + b = - 2 a + 75$

$b = - 2 a + 75$

Step 2) Substitute $\left(- 2 a + 75\right)$ for $b$ in the second equation and solve for $a$:

$a + b + 6 = 54$ becomes:

$a + \left(- 2 a + 75\right) + 6 = 64$

$a - 2 a + 75 + 6 = 64$

$1 a - 2 a + 75 + 6 = 64$

$\left(1 - 2\right) a + 81 = 64$

$- 1 a + 81 = 64$

$- a + 81 - \textcolor{red}{81} = 64 - \textcolor{red}{81}$

$- a + 0 = - 17$

$- a = - 17$

$\textcolor{red}{- 1} \cdot - a = \textcolor{red}{- 1} \cdot - 17$

$a = 17$

Step 3) Substitute $17$ for $a$ in the solution to the first equation at the end of Step 1 and calculate $b$:

$b = - 2 a + 75$ becomes:

$b = \left(- 2 \cdot 17\right) + 75$

$b = - 34 + 75$

$b = 41$

The solution is:

Albert is 17 and Bob is 41