Algebra. Please show work and really break it down

Question

Last season two running backs on the Steelers football team rushed for a combined total of 1550 yards. One rushed 4 times as many yards as the other. How many yards were rushed by each player.

Answer 1

Hello.

 

Okay, so there are two things we need to know here, the number of yards rushed by player a (let's just call this number a), and the number of yards rushed by player b (let's just call this number b).  Here is a rule in algebra, to find two unknown things, you always need two equations.

 

Each of the first two sentences is giving you an equation.  Sentence one:

 

"Last season two running backs on the Steelers football team rushed for a combined total of 1550 yds."

 

This means the number of yards rushed by player a plus those rushed by player b equals 1550:

a+b=1550.

 

Sentence two:

"One rushed 4 times as many yards as the other."

This means one of those numbers (say a) is 4 times larger than the other (b), or

4*a=b.

 

Great, now we have two equations.  This is where we actually do algebra.  The second equation (the one I just wrote) means I can replace b with 4*a, so I'm going to do that in the first equation.  That makes the first equation look like this:

 

a+(4*a)=1550.

 

Now I have one a and four more a's, so that's 5*a=1550.

5*a=1550.

Now I divide both sides by 5:

a=310.

 

Great! Player a rushed 310 yards.  Now, to figure out how many yards player b rushed, we have to use the second equation.

4*a=b

4*(310)=b

1,240=b

So player b rushed 1,240 yards.  Let's make sure that adds up to 1550

1,240+310=1550

Yep.

 

Solution

Player a rushed 310 yards, Player b rushed 1,240 yards