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#. And, let's call Bob's age: #b#

Now, we can write:

#2a + b = 75#

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

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

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

#0 + b = -2a + 75#

#b = -2a + 75#

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

#a + b + 6 = 54# becomes:

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

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

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

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

#-1a + 81 = 64#

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

#-a + 0 = -17#

#-a = -17#

#color(red)(-1) * -a = color(red)(-1) * -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 = -2a + 75# becomes:

#b = (-2 * 17) + 75#

#b = -34 + 75#

#b = 41#

The solution is:

Albert is 17 and Bob is 41