What's Peter's weight in pounds?

Question

John's weight is 3/5 of Peter's weight. If John were to gain 8 pounds, he'd weigh 2/3 of Peter's weight. What's Peter's weight in pounds?

Answer 1

Hi! I'm Stephanie.

 

This problem looks a little scary, but it's not bad if you break it down. It needs to be solved using a system of two equations. Lets start with the first part of this question. "John's weight is 3/5 of Peter's weight." Lets use J for John an P for Peter. So, John is 3/5 of Peter;

 

J=3/5P

 

Now, for the second part: "If John were to jain 8 pounds, he'd weigh 2/3 of Peter's weight." So;

 

J+8=2/3P

 

Now, what we're trying to figure out is Peter's weight.

 

We already know that J=3/5P from the first equation. What we're going to do is use what's called the substitution method. Look at this:

 

3/5P+8=2/3P

 

Here, we have replaced the J in the second equation, with 3/5P, because as we know, they are equivalent. So now all we have left is simply solving the equation.

 

3/5P    +8  =  2/3P       → 2/3-3/5=1/15

-3/5P             -3/5P

 

8    = 1/15P

1/15  1/15

 

120=P

 

Now, we know that Peter weighs 120 pounds. Now, lets check our answer using the original two equations.

 

J=3/5(120)

J=72

 

J=2/3(120)-8

J=80-8

J=72

 

So, now that we know that the equations work, we know the final answer to the problem:

 

Peter weights 120 pounds.