Please help me breakdown the steps to solve this problem.

Question

The cross country teams of east high and west high run against each other twice each fall. At the first meet,East's score was two thirds of West's score. At the second meet, East's score increased by seven points and West's score decreased by seven points. In the second meet West's score was three less than East's score. How many points did each team score in each meet?

Answer 1

OK, Sheila, I hope I'm not too late to help.

 

In a word problem, the word "of" always means to multiply.  If we let e = East's original score and w = West's original score, then e = 2/3w.

 

In the second meet, East's score becomes e + 7 and West's score becomes w - 7, right?  Now, if they tied in the 2nd meet, we'd have e+7 = w - 7, right?  

 

Buuuut, we have to subtract three points from East's score to get West's score, since West's new score is three less than East's.  Now we have e + 7 - 3 = w - 7, or e + 4 = w - 7.

 

Now, we can substitute the e in the first equation into the second equation.  2/3w + 4 = w - 7.  1/3w = 11, so w = 33.

 

So, West scored a 33 in the first meet.  2/3(33) = 22, so East scored a 22.  In the second meet, West scored a 26 and East scored a 29.

 

Hope this helps!