How much did each boys fish weigh?

Question

Pacey, Alex, and Paul went fishing. They each caught one fish. Alex's weighed twice as much as Pacey's fish. Pauls weighed three times as much as Pacey's fish. Total the 3 fish weighed 342 lbs.

Answer 1

Hi Patty, I love these kinds of word problems.  Yes, I'm a nerd.

Let's treat Pacey, Alex, and Paul as just letters instead of treating them like people.  It's okay -- they're imaginary, so I don't think they'll mind.  Pacey will be X, Alex will be Y, and Paul will be Z.  In a math book, it might look something like this:

Pacey = x

Alex = y

Paul = z

 

Now we can translate all those words in the problem into numbers (and variables).  We know that all together, the 3 fish weigh 342 lbs:

 

x + y + z = 342

 

We also know that Alex (y)'s fish weighed twice as much as Pacey (x)'s:

 

y = 2x

(This is the part a lot of students get confused about, so if you have trouble at this step, let me know and we'll talk about it more.)

 

Of course, I won't put the entire answer here for you, because that would take all the fun out of you arriving at the solution yourself and feeling all awesome and accomplished and super-smart for doing so.  However, now that we know how to rewrite Alex's fish as "y=2x", is there a way we can rewrite Paul's fish in a similar manner?  After that, is there a way we can rewrite the first equation, "x+y+z=342", in a way that looks a lot more friendly (perhaps using just one letter instead of dealing with three different ones)?