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Q In a group of 150 students, more students are taking a math class than are taking a science class this semester

. In a group of 150 students, more students are taking a math class than are taking a science class this semester. If 80 are taking a science class and 25 are not taking either math or science this semester, what is the minimum number of students who could be taking both math and science this semester?

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#1kimaniAnswered at 2013-02-09 05:24:56
In a group of 150 students, more students are taking a math class than are taking a science class this semester. If 80 are taking a science class and 25 are not taking either math or science this semester, what is the minimum number of students who could be taking both math and science this semester? <pre><font size = 3 color = "indigo"><b> There are four categories of students here: 1. Those taking math but not science. 2. Those taking science but not math. 3. Those taking both math and science. 4. Those taking neither math nor science. 1. Let x = the number of students taking math but not science. 2. Let y = the number of students taking science but not math. 3. Let z = the number of students taking both math and science. 4. Let w = the number of students taking neither math nor science. We are asked: >>.....what is the minimum number of students who could be taking both math and science this semester?.....<< So we want to know the smallest possible value of z. >>......In a group of 150 students,......<< Therefore, x + y + z + w = 150 >>......more students are taking a math class than are taking a science class this semester......<< Therefore x + z > y + z. Subtracting z from both sides, x > y >>......If 80 are taking a science class......<< Therefore y + z = 80 >>......and 25 are not taking either math or science this semester,......<< Therefore w = 25 So we have these four facts: x + y + z + w = 150 x > y y + z = 80 w = 25 Substituting w = 25 in the first equation, x + y + z + 25 = 150 x + y + z = 125 Substitute 80 for y + z in that: x + 80 = 125 x = 45 Substitute x = 45 in x > y 45 > y Solve y + z = 80 for y y = 80 - z Substitute 80 - z for y in 45 > y 45 > 80 - z z > 80 - 45 z > 35 So the minimum value of z is 36, for that is the smallest possible whole number greater than 35. Edwin</pre>
#2factoring! help! urgent!! :(Answered at 2013-02-13 16:53:25
There are four categories of students here: 1. Those taking math but not science. 2. Those taking science but not math. 3. Those taking both math and science. 4. Those taking neither math nor science. 1. Let x = the number of students taking math but not science. 2. Let y = the number of students taking science but not math. 3. Let z = the number of students taking both math and science. 4. Let w = the number of students taking neither math nor science. We are asked: >>.....what is the minimum number of students who could be taking both math and science this semester?.....<< So we want to know the smallest possible value of z. >>......In a group of 150 students,......<< Therefore, x + y + z + w = 150 >>......more students are taking a math class than are taking a science class this semester......<< Therefore x + z > y + z. Subtracting z from both sides, x > y >>......If 80 are taking a science class......<< Therefore y + z = 80 >>......and 25 are not taking either math or science this semester,......<< Therefore w = 25 So we have these four facts: x + y + z + w = 150 x > y y + z = 80 w = 25 Substituting w = 25 in the first equation, x + y + z + 25 = 150 x + y + z = 125 Substitute 80 for y + z in that: x + 80 = 125 x = 45 Substitute x = 45 in x > y 45 > y Solve y + z = 80 for y y = 80 - z Substitute 80 - z for y in 45 > y 45 > 80 - z z > 80 - 45 z > 35 So the minimum value of z is 36, for that is the smallest possible whole number greater than 35. Edwin
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