Sharpen your understanding of ratios and proportions with practical problems involving comparisons, scaling, and real-life scenarios. This quiz assesses key concepts such as simplifying ratios, cross-multiplying, solving word problems, and identifying proportional relationships.
If the ratio of boys to girls in a class is 15:25, what is the simplest form of this ratio?
Explanation: The simplest form of the ratio 15:25 is obtained by dividing both numbers by their greatest common divisor, which is 5, resulting in 3:5. Option 5:3 is a reversal of the correct ratio and does not reflect the correct relationship. 15:10 is not equivalent to 15:25, and 5:8 is not the right simplification. Therefore, 3:5 is correct.
Which of the following sets represents a proportion: 6:9 = 10:15?
Explanation: Both 6:9 and 10:15 simplify to 2:3, confirming that these ratios form a proportion. The option stating the numbers are not multiples of each other is incorrect because it's the simplest form that matters, not multiples. 6:9 does not simplify to 1:1.5, making that distractor invalid. While 6 does not divide exactly into 10, even if it did, that would not alone confirm proportionality.
If 12 apples cost $18, how much would 20 apples cost, assuming the price is proportional?
Explanation: Since the cost is proportional, set up a proportion: 12/18 = 20/x. Cross-multiplying gives 12x = 360, so x = $30. $36 comes from mistakenly multiplying 18 by 2, not by the correct ratio. $24 and $32 are not in the correct proportion to the initial cost. Thus, $30 is the correct answer.
A recipe uses flour and sugar in the ratio 7:3. If 350 grams of flour are used, how much sugar is needed?
Explanation: Set up a proportion: 7 parts flour corresponds to 3 parts sugar, so (flour/sugar) = 7/3. If 350 grams of flour is used, divide by 7 to get 50 grams per part, and multiply by 3 parts of sugar to get 150 grams. 120 grams and 90 grams result from using the wrong part value, and 100 grams comes from simply dividing or misreading the ratio. Therefore, 150 grams is correct.
A map uses a scale of 1:200,000. If two cities are 6 centimeters apart on the map, what is the real distance between them in kilometers?
Explanation: A scale of 1:200,000 means 1 cm on the map equals 200,000 cm in reality. 6 cm on the map equals 1,200,000 cm, which converts to 12,000 meters or 120 kilometers. Options 12 km and 1.2 km are the result of misplacing the decimal. 60 km is a calculation error, possibly from halving or misapplying the conversion. Only 120 km is correct.