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?

Question

1407 views around the world

You can reuse this answer
Creative Commons License

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