1250 oranges were distributed among a group of girls of a class. Each girl got twice as many oranges as the number of girls in that group. The number of girls in the group was

### Concept & Logic This is a straightforward algebra problem where the quantity distributed per person depends directly on the total number of people. It requires setting up a basic quadratic equation and solving for the positive root. ### Step-by-Step Solution * Let the total number of girls in the group be $x$. * **Given:** Each girl received twice as many oranges as the total number of girls. * Therefore, oranges received by one girl = $2x$. * The total number of oranges distributed is the product of the number of girls and the oranges per girl: * Total Oranges = (Number of girls) $\times$ (Oranges per girl) * Total Oranges = $x \cdot 2x$ * $2x^2 = 1250$ * Divide both sides by 2 to isolate $x^2$: * $x^2 = 625$ * Take the square root of both sides to find $x$: * $x = \sqrt{625}$ * We know that $25 \times 25 = 625$. * $x = 25$. ### Exam Strategy & Shortcut You can solve this rapidly using the options. The total oranges ($1250$) must be equal to $2x^2$. Divide the total by 2 in your head to get $625$. Now, you just need to identify which option is the square root of $625$. $50^2 = 2500$ (Too big) $45^2 > 40^2 = 1600$ (Too big) $25^2 = 625$. (Perfect match). ### Common Pitfall The most common trap is forgetting to include the multiplier "twice as many". If a student misreads it as "as many oranges as the number of girls", they will set up $x^2 = 1250$, which doesn't have an integer square root, causing confusion and wasted time. Always pay close attention to proportional keywords like "twice" or "half". ### Final Answer **Therefore, the correct answer is 25.**