Oranges are to be transferred from larger boxes into small boxes. When a large box is emptied, the oranges from it fill two smaller boxes and 10 oranges remain. If the number of or... Oranges are to be transferred from larger boxes into small boxes. When a large box is emptied, the oranges from it fill two smaller boxes and 10 oranges remain. If the number of oranges in a small box is 'x', what is the number of oranges in a larger box?
Understand the Problem
The problem describes a scenario where oranges are transferred from a large box to smaller boxes. The question asks us to express the number of oranges in the larger box in terms of 'x', where 'x' represents the number of oranges in a small box. After filling two smaller boxes with oranges from the larger box, there are 10 oranges left over.
Answer
$2x + 10$
Answer for screen readers
$2x + 10$
Steps to Solve
- Define the variable
Let $x$ be the number of oranges in one small box.
- Calculate the total number of oranges in two small boxes
Since there are two small boxes, the total number of oranges in them is $2 \times x = 2x$.
- Express the number of oranges in the large box
The number of oranges in the large box is equal to the number of oranges in the two small boxes plus the 10 oranges that are left over. So, the number of oranges in the large box is $2x + 10$.
$2x + 10$
More Information
The expression $2x + 10$ represents the total number of oranges that were originally in the larger box. For example, if each small box contains 5 oranges ($x = 5$), then the larger box originally contained $2(5) + 10 = 10 + 10 = 20$ oranges.
Tips
A common mistake is to only consider the number of oranges in one small box, forgetting to account for both boxes. Another mistake could be subtracting 10 from $2x$ instead of adding it, not understanding that the 10 oranges are left over after filling the small boxes.
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