If the numerator of a fraction is increased by 3 , the fraction becomes \( 3 / 4 \). If the denominator is decreased by 7 , the fraction becomes 1 . What is the numerator of the fraction? 2 9 9

To solve this puzzle, let’s turn it into a little detective work! We can denote the original fraction as \( \frac{x}{y} \). According to the first clue, if we add 3 to the numerator, we get \( \frac{x + 3}{y} = \frac{3}{4} \). This gives us the equation \( 4(x + 3) = 3y \). The second clue states that if we reduce the denominator by 7, we achieve \( \frac{x}{y - 7} = 1 \), leading to \( x = y - 7 \). Now, with a bit of substitution and solving, you'll find that the numerator \( x \) equals 9. Mystery solved! Math not only plays a significant role in academia but also in real-life situations! For instance, understanding fractions is essential in cooking when adjusting ingredient amounts, budgeting finances, or even in construction when measuring lengths. So the next time you’re following a recipe or balancing your budget, remember the handy work of fractions—and that little extra math will help ensure you're on the right track!