A certain science class has a total of 35 students. If the ratio of girls to boys in the class is 4 : 3, how many more girls than boys are in the class? A. 1 B. 5 C. 7 D. 15 E. 20
(B) If there are 4 girls for every 3 boys, then the class is 4/7 girls and 3/7 boys. The number of girls in the class is 4/7 × 35 = 20, and the number of boys is 3/7 × 35 = 15. The question asks how many more girls there are than boys: 20 – 15 = 5 more girls than boys. The correct answer is choice (B). ---------- I do not understand why the explanation can use ratio 3/7 and 4/7. Because I read an information, sound likes if girls is A, boys is B => A/B = 4/3. So I can solve with two conditions such as A/B = 4/3 and A + B = 35. Hence, B = 15, A = 20.
because I read an information, sound likes if girls is A, boys is B => A/B = 4/3.
You use the classical ratio approach. A : B = 4 : 3. That's completely fine and works here well. Note, that you get the same result. A – B = 20 – 15 = 5 more girls than boys.
I do not understand why the explanation can use ratio 3/7 and 4/7.
How do we get 3/7 and 4/7 so fast, knowing the ratio 3 : 4? The ratio 3 : 4 gives us: boys = 3x, girls = 4x. The total number of students is 3x + 4x = 7x So boys make 3x/7x = 3/7. Girls make 4x/7x = 4/7.
So if we know that some total set is composed of just A and B in ratio a : b, then A makes a/(a + b) and B makes b/(a + b) of the whole.
Furthermore, it is true for any number of subset objects. Just make sure they all compose the whole set. For example, If an alloy is composed of three elements in ratio 2 : 3 : 4, then element 1 is 2/9 of the alloy element 2 is 3/9 of the alloy element 3 is 4/9 of the alloy
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