Rebecca has left three bags containing the same number of marbles, plus two marbles left over. She places them on one side of a balance. Chris, who has more marbles than Rebecca, adds marbles to the other side of the balance. He finds that with 29 marbles, the scale balance. How many marbles are in each bag?Assume the bags weigh nothing.
let x = # marbles in bag.
3x + 2 = 29
Solve for x.
number of marbles in each bag --- x
3x + 3 = 29
3x=27
x=9
each bag has 9 marbles
Go with PsyDAG's solution, I hit the 3 key instead of the 2
To solve this problem, we can break it down into steps and use logical reasoning.
Let's assume the number of marbles in each bag is "x".
According to the problem, Rebecca has three bags with the same number of marbles, plus two marbles left over. So, we can write the equation:
3x + 2 = total number of marbles Rebecca has
Next, we know that Chris has more marbles than Rebecca and adds marbles to the other side of the balance. When the scale balances, it means that the total number of marbles on each side of the balance is the same.
So, the equation becomes:
3x + 2 = x + 29
Now we can solve this equation for x:
3x - x = 29 - 2
2x = 27
x = 27 / 2
x = 13.5
Since we cannot have half a marble, we can conclude that there are no solutions to this problem. The problem might have an error or was not intended to have a solution with whole numbers.
If you encounter a similar problem in the future, carefully review the information given and check if there might be any errors or missing details.