Twenty years ago I was twice as old as Jake. In four years the sum of jakes and bobs ages will be 49. If I was fourteen when bob was born how old am I now

Question

20 years ago I was twice as old as Jake. In four years the sum of jakes and bob ages will be 49. If I was 14 when bob was born how old am I now?

Answer 1

It helps to start by defining variables.

 

Let x equal how old I am now.

Let j equal Jake's age.

Let b equal Bob's age.

 

Then translate the sentences into math sentences.

 

20 years ago I was twice as old as Jake. --> x-20=2(j-20)

In four years, the sum of Jake's and Bob's ages will be 49. --> j+4+b+4=49

If I was 14 when Bob was born, how old am I now?

This requires a little extra logic. Really, all this sentence means is that I am 14 years older than Bob.--> x=b+14

 

Now we have three variables and three number sentences, so we can solve. First, look at the last statement: x=b+14. It's the simplest statement involving x. You can solve for b, then replace b in the second sentence:

x=b+14

b=x-14   Solve for b.

j+4+b+4=49

j+b+8=49   Simplify.

j+x-14+8=49    Replace b with x-14.

j+x-6=49

j+x=55   Simplify.

 

Now you can solve for j and replace j in the first number sentence to solve for x.

 

j+x=55

j=55-x   Solve for j.

x-20=2(j-20)

x-20=2(55-x-20)   Replace j with 55-x.

x-20=2(35-x)  Simplify.

x-20=70-2x   Get the terms with x on one side and the terms without on the other by adding 2x and 20 to both sides.

3x=90

x=30

 

Check! Since you created the number sentences, check back with the logic of the original word problem.

20 years ago I was twice as old as Jake.-->If I am 30, then 20 years ago I was 10. If I was twice as old as Jake, he was 5. Now he must be 25.

If I was 14 when Bob was born, how old am I now?--> Well, I'm 30 now, so if I'm 14 years older than Bob, Bob is 16. We need this to check the second sentence.

In four years, the sum of Jake's and Bob's ages will be 49. --> In four years, Jake will be 29 and Bob will be 20. 29+20=49, so it works out!

 

The only really tricky bit here is the first sentence. If 20 years ago I was twice as old as Jake, then should the equation be x-20 (my age minus 20 years)=             

2(j-20) (twice Jake's age 20 years ago)

or

2(j) (twice Jake's current age).

In order for the second option to be true, the question should read: 20 years ago I was twice as old as Jake is now. Since it doesn't say that, you can safely assume the first interpretation is likely correct.