Question

Coach Johnson is 10 years older than Tim. When Tim started football 3 years ago, Coach Johnson was twice his age. How old is Tim now?

Answer 1

Set a up a system of equations. Lets let Tim = (x) years old and Coach Johnson will be (y) years old. We know that Coach Johnson is 10 years older than Tim, so:

y = x + 10

next we know that 3 years ago, Coach Johnson was twice as old as Tim so:

y - 3 = 2(x - 3)

Now lets set up an equation in the terms of one variable. Since we know y = x + 10, lets plug that into our second equation:

(x + 10) - 3 = 2x - 6

x + 10 - 3 = 2x - 6

Now we just need to isolate and solve for (x)

x + 7 = 2x - 6

x = 2x - 6 -7

x = 2x - 13

x - 2x = - 13

-x = -13

x = 13

So Tim is 13 years old which means Coach Johnson is (13) + 10 = 23 years old