I am trying to build and solve and equation from a word problem.

Question

Brian is 48 and Meagan is 24.  At some point during their lives Brian will be three times older than Meagan.  Write an equation which models how old in years both Brian and meagan will be when Brian is three times older than Meagan.

Answer 1

I like to use variables that remind me what they represent, so let's use B for Brian's age and M for Meagan's age. We know that:

B = 48

and

M = 24

What we do not know is how many years we are adding.  So the number of years is Y.

So Brian's age plus some number of years equals 3 times Meagan's age plus that number of years. In math terms:

B + Y = 3(M + Y)

You can substitute in their ages:

48 + Y = 3(24 + Y)

 To solve it, use distributive property on the right:

48 + Y = 72 + 3Y

Use subtraction to get the Ys on one side and constants on the other:

48 + Y -3Y = 72 +3Y -3Y

gives you:           48 - 2Y = 72

then:               48 -48 - 2Y = 72 -48

so:          -2Y = 24

then divide by -2:

-2Y / -2 = 24 / -2

Y = -12

which means that 12 years AGO, Brian was 3 times older than Meagan, when Brian was 36 and Meagan was 12.

Hope this helped!

Kathye

Answer 2

Mental math approach:

Since Brian is 48 and Meagan is 24, Brian is 24 years older than Meagan. First, this can not happen in the future becaues the ratio of Brian's age to Meagon's is becoming smaller and smaller in the future. So, it must have happened before. When Brian's age is three times the Meagan's age, the 24 year difference should be twice the Meagon's age.Therefore, Meagon's age was 12 years old.

Answer: This happened 12 years ago.