Final Answers:
(a) The number is 40. Therefore, 35% of 40 is indeed 14.
(b) 65% of 60 is 39. Hence, 65% of 60 equals 39.
Step-by-step explanation:
(a) To find 35% of a number that equals 14, we can set up the equation frac{35}{100} \times x = 14, where x represents the unknown number. To solve for x, multiply both sides of the equation by frac{100}{35}, yielding x = frac{14 \times 100}{35} = 40. Therefore, 35% of 40 is indeed 14.
(b) To determine 65% of 60, simply multiply 60 by 0.65 (or 65%). Mathematically, 65% \times 60 = frac{65}{100} \times 60 = 39. Hence, 65% of 60 equals 39.
In part (a), to calculate the number representing 35% of an unknown value, I utilized the formula for finding a percentage of a number. Setting up the equation frac{35}{100} \times x = 14 allows solving for the unknown number x. By multiplying both sides by frac{100}{35}, we find the number to be 40.
Regarding part (b), finding 65% of 60 involves straightforward multiplication. Multiplying 60 by 0.65 (or converting 65% to its decimal form) results in 39. This demonstrates that 65% of 60 indeed equals 39, showcasing the direct application of percentages in numerical calculations.
Understanding percentages is crucial in various real-life scenarios, from financial calculations to everyday problem-solving. Mastery of percentage calculations aids in making informed decisions and interpreting data accurately.