How old is each of the boys now?

Question

Lucas is 10 years older than Braden. In five years Lucas will be 6 years less than twice the age of Braden. How old are the boys now? 

 

This is what I have so far. 

 

                 Now.            +5years

Lucas.      B+5                2(B+15)-6

Braden       B                   B+5

 

I don't know how to solve without their total ages together... Please help?

 

                                                      

                                                                      

Answer 1

HI Hazel, 

 

I'd set the problem up as below:

 

Lucas  = L

Braden = B

 

The text tells us that Lucas is 10 years older than Braden.  So, 

 

L= B +10

 

Additionally, we know that in 5 years, Lucas will be twice Braden's age.  So, 

 

L+5=2B

 

I'd solve the above equation, for L, which would yield L=2B-5

 

Since we now have two equations equal to L, we can set them equal to each other:

 

B+10=2B-5

**subtract B from each side of the equation, to get

10=B-5

**add 5 to each side of the equation to get, 

15=B

 

Substitute your new value for B into the first equation:

 

L=B+ 10 --> L=15+10 --> L=25

 

Therefore, Lucas is 25 years old and Braden is 15 years old.