a basketball team played 74 games. They won 28 more than they lost. How many did they win?

Question

Story problem 

Answer 1

The key to word (story) problems is to translate the words and phrases into precise, concise math expressions (variables with operations).

 

Read the problem until you understand it.  Put it into your own words.  I might say, "In a season of 74 games, the basketball team lost some games, but they won 28 more than they lost.  How many did they win?"

 

Then, assign variables.  If possible, assign a variable to the value the problem asks you to find.  Here, let:

     W = number of wins

     L = number of losses   (actually, we don't need L if we use 74-W immediately)

 

Translate:

  "basketball team played 74 games"    means   W + L = 74     (eq1)

  "won 28 more than they lost"     means     W = 28 + L             (eq1)

 

Now, the easy math:

      W + L = 74         (eq1)

      W  - L = 28         (re-written eq2)

  --------------------   (elimination method: add equations)

      2W     = 102

       W = 51             (divide both sides by 2)

 

The problem does not require us to determine L, but you can if you want to check your answer.

Answer 2

let w = wins

let l = losses = 74-w

w-l = 28 = w-(74-w) = 2w -74

2w = 102

w = 51 = number of games won

l = 74-51 = 23

 

Answer 3

You can set up a system of equations to solve for the number of wins. If wins = W and losses = L, then W + L = 74 as there are a total of 74 games played. If the team won 28 more games than they lost, this translates into L + 28 = W. 

 

You can then solve the system by substituting L + 28 into the first equation in the place of W. This gives you the equation (L + 28) + L = 74. From there, solve for the number of losses. 2L + 28 = 74; 2L = 46; L = 23. 

 

If there are 23 losses, that means you will add 23 + 28 (28 more wins than losses) to receive the number of wins. W = 51.