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Algebra Word Problems

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2 Answers

Here is what you know from the problem.

  • The total earned for the two games is $3,482.50. 
  • The amount earned for one game is $557. 50 more that the amount earned for the other one.

Here is what you want to know.

  • How much money was earned for each game? If the same amount was earned for each game, you would just divide the total earned by 2.

Since the amounts are different, where do you start? If you know the amount earned in one game, you can figure out the amount earned in the other game.

Let “x” represent the amount earned for one of the games, the one that earned less for the team. Then “x + $557.50” represents the amount earned for the other game. When you add these amounts together, you will have the total earned for the two games, $3482.50.

Your equation is:

x + (x + $557.50) = $3,482.50

Step 1. Follow the order of operations. First solve what is inside the parentheses to remove them. (Remember, "Please Excuse My Dear Aunt Sally, or, Parentheses, Exponents, Multiply, Divide, Add, Subtract.)

x + x + $557.50 = $3,482.50

Step 2. Combine like terms. In this problem, that is the x’s.

2x + $557.50 = $3,482.50

Step 3. Isolate the term with the variable x, that is 2x, by subtracting $557.50 from both sides of the equation.

2x + $557.50 (- $557.50) = $3,482.50 (- $557.50)

2x + $0 = $2925.00

Step 4. Solve for x by dividing both sides of the equation by 2.

2x (÷ 2) = $2950.00 (÷ 2)

x = $1,462.50 This is the amount earned for one of the games

Step 5. Replace the x with the amount you now know it stands for.

x + $557.50

$1,462.50 + $557.50 = $2,020.00,  the amount earned for the other game

game.

Step 6. Check your results. Do the 2 amounts total $3,482.50?

   $1,462.50 + $2,020.00 = $3,482.50

First, assign variables to each parameter. That is, let

          x = Friday's game          and          y = Saturday's game

We are given that the two games together earn the team $3482.50, then

               x + y = 3482.50

Since we have two unknown variables, we will need to solve for one variable first then we will be able to solve for the other. The problem states that the total earnings from Friday's game (x) is equal to $557.50 less than the total earnings from Saturday's game (y), which translates to the following:

          x = y - 557.50

Looking back at the equation formed for the total earnings of both games, we can substitute the equation above for x (which is basically x in terms of y). That is,

          x + y = 3482.50

          y - 557.50 + y = 3482.50

          y + y - 557.50 = 3482.50

          2y - 557.50 = 3482.50

Now that we have an equation with only one unknown variable (y), we can solve for y then use the value of y to solve for x.

          2y - 557.50 = 3482.50

          2y - 557.50 + 557.50 = 3482.50 + 557.50

          2y = 4040

          2y/2 = 4040/2

           y = 2020

Use the equation we found for x to solve for this variable using the solution for y:

          x = y - 557.50

          x = 2020 - 557.50

          x = 1462.50

Therefore, 

   x = Friday's game = 1462.50   ==>   Friday's game brought in $1462.50

   y = Saturday's game = 2020   ==>   Saturday's game brought in $2020.00