Ted has twice as many baseball cards as Bob. Reggie has five less than Ted. How many baseball cards does Ted have if Reggie and Bob have 82 cards altogether? Explain the process you used to solve this problem.
Bob: X baseball cards.
Ted: 2x " "
Reggie: 2x-5 " "
2x-5 + x = 82.
X = ?.
2x = ?
To solve this problem, we can use algebraic equations. Let's assign variables to the unknown quantities:
Let "x" represent the number of baseball cards Bob has.
Since Ted has twice as many cards as Bob, Ted will have "2x" cards.
And Reggie has five less than Ted, so Reggie will have "2x - 5" cards.
We know that Bob, Ted, and Reggie have a total of 82 cards altogether, so we can write the equation:
x + (2x) + (2x - 5) = 82
Now we can solve for x:
Combining like terms, we have:
5x - 5 = 82
Add 5 to both sides of the equation:
5x = 87
Finally, divide both sides of the equation by 5:
x = 17.4
Since we can't have a fraction of a baseball card, we round up to the nearest whole number:
x ≈ 18
So, Bob has 18 baseball cards.
Now we can find out how many cards Ted has:
Ted has twice as many cards as Bob, so Ted will have 2x:
Ted = 2 * 18 = 36
Therefore, Ted has 36 baseball cards.