Answer:
a. 41 students decided to study nursing
Step-by-step explanation:
The given are 164 total number of students, [tex]\frac{2}{4}[/tex] will take technical courses and [tex]\frac{1}{4}[/tex] will take education. We need to know how many students will enroll in nursing.
Step 1: Write the mathematical equation of the problem. Let x be the number of students who will enroll in nursing. Thus,
[tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] + x = 1
Step 2: Notice that the given fractions have the same denominator. Hence, our least common denominator will be 4. Solving for x will be,
x = 1 - [tex]\frac{2}{4}[/tex] - [tex]\frac{1}{4}[/tex]
x = [tex]\frac{4 - 2 - 1}{4}[/tex] = [tex]\frac{1}{4}[/tex] x 164 = 41 students
Let us check our answer:
164 x [tex]\frac{2}{4}[/tex] = 82 students ; 164 x [tex]\frac{1}{4}[/tex] = 41 students
164 - 82 - 41 = 41 students will enroll in nursing
Therefore, [tex]\frac{1}{4}[/tex] of 164 students or 41 students will enroll in nursing.
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