How to use bar models to understand how much apples are in two baskets knowing how many there are in total and that if you take a certain number from the first one to the second make them equal?
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Welcome to bar models! Today we'll solve a problem about apple distribution. We have two baskets with 20 apples total. If we move 3 apples from the first basket to the second, they become equal. Let's use bar models to find how many apples are in each basket originally.
First, let's visualize what happens after moving the apples. When both baskets have equal amounts, and the total is 20 apples, each basket must contain 10 apples. We can represent this with a bar model divided into two equal parts.
Now we work backwards to find the original amounts. Since basket 1 gave away 3 apples to end up with 10, it originally had 13 apples. Since basket 2 received 3 apples to end up with 10, it originally had 7 apples. The bar model shows this transfer clearly.
Let's verify our solution. Originally, basket 1 had 13 apples and basket 2 had 7 apples, totaling 20 apples. After moving 3 apples from basket 1 to basket 2, basket 1 has 10 apples and basket 2 has 10 apples. Both conditions are satisfied, so our solution is correct!
Bar models give us a general approach for these problems. For any total T and transfer amount X, each basket has T divided by 2 after the transfer. The original larger basket had this amount plus X, and the smaller basket had this amount minus X. This visual method makes complex word problems much easier to understand and solve!