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?

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Answer 1 · 2017-06-15T12:57:07

See a solution process below:

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

Now, we can write:

$2 a + b = 75$ $2a + b = 75$

$(a + 3) + (b + 3) = 64$ $(a + 3) + (b + 3) = 64$ or $a + b + 6 = 64$ $a + b + 6 = 64$

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

$- 2 a + 2 a + b = - 2 a + 75$ $-color(red)(2a) + 2a + b = -color(red)(2a) + 75$

$0 + b = - 2 a + 75$ $0 + b = -2a + 75$

$b = - 2 a + 75$ $b = -2a + 75$

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

$a + b + 6 = 54$ $a + b + 6 = 54$ becomes:

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

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

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

$(1 - 2) a + 81 = 64$ $(1 - 2)a + 81 = 64$

$- 1 a + 81 = 64$ $-1a + 81 = 64$

$- a + 81 - 81 = 64 - 81$ $-a + 81 - color(red)(81) = 64 - color(red)(81)$

$- a + 0 = - 17$ $-a + 0 = -17$

$- a = - 17$ $-a = -17$

$- 1 \cdot - a = - 1 \cdot - 17$ $color(red)(-1) * -a = color(red)(-1) * -17$

$a = 17$ $a = 17$

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

$b = - 2 a + 75$ $b = -2a + 75$ becomes:

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

$b = - 34 + 75$ $b = -34 + 75$

$b = 41$ $b = 41$

The solution is:

Albert is 17 and Bob is 41