During her tennis career a player won a total of 61

Question

During her tennis career a player won a total of 61 grand slam titles in three catigories; womens singles womens doubles and mixed doubles. out of this total her number of wins in womens singles is 9 more than her number of wins in mixed doubles. her number of wins in woumens doubles is two more than three time her number of wins in mixed doubles. how man did the player win in each category

Answer 1

Hi Brandon,

 

Let's begin by assigning letters to represent our three unknowns:

    x = number of wins in women's singles

    y = number of wins in mixed doubles

    z = number of wins in women's doubles

 

Now let's see how we can represent all three unknowns in terms of just one unknown:

    x = y + 9 (nine more wins)

    z = 3y + 2 (two more wins than 3 times wins)

 

We now have all three unknowns expressed in terms of unknown (y), so let's write our equation to represent the total number of wins in terms of unknown (y):

    x + y + z = 61 

    (y + 9) + y + (3y + 2) = 61 (our equation)

 

Now let's solve our equation for unknown (y) and then use our value for y to determine the values for our other two unknowns:

    (y + 9) + y + (3y + 2) = 61 (our equation)

    y + 9 + y + 3y + 2 = 61

    5y + 11 = 61

    5y = 61 - 11

    5y = 50

      y = 50/5

       y = 10 (number of wins in mixed doubles)

      x = y + 9

      x = 10 + 9

      x = 19 (number of wins in women's singles)

      z = 3y + 2

      z = 3(10) + 2

      z = 30 + 2

      z = 32 (number of wins in women's doubles)

 

Finally, we can check to see if answers are correct by seeing if their sum equals the total number of wins:

     x + y + z = 61

     19 + 10 + 32 = 61

     29 + 32 = 61

     61 = 61 (sum of category wins equals
                      total wins)

 

Their sum does match the total, so we are confident our answers are correct.

 

The trick to solving this problem was realizing that we could express all three unknowns in terms of just one unknown in order to come up with a solvable equation.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.