A baseball team has home games on Friday and Saturday. The two games together earn $3482.50 for the team. Friday's game generates $557.50 less than Saturday's game. How much money was taken in each game?
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
Step 6. Check your results. Do the 2 amounts total $3,482.50?
$1,462.50 + $2,020.00 = $3,482.50