Multiple Choice
Which of the following statements is true about scarcity?
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0. Basic Principles of Economics
Scarcity and Choice
Multiple Choice
Which of the following ratios is equivalent to '4 pencils for every 2 students'?
A
8 pencils for every 4 students
B
2 pencils for every 1 student
C
1 pencil for every 2 students
D
2 pencils for every 4 students
Verified step by step guidance1
Step 1: Understand the given ratio '4 pencils for every 2 students' as a fraction representing pencils per student: \(\frac{4 \text{ pencils}}{2 \text{ students}}\).
Step 2: Simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 2, resulting in \(\frac{4 \div 2}{2 \div 2} = \frac{2 \text{ pencils}}{1 \text{ student}}\).
Step 3: To check for equivalent ratios, multiply or divide both parts of the ratio by the same number. For example, multiplying both numerator and denominator by 2 gives \(\frac{2 \times 2}{1 \times 2} = \frac{4 \text{ pencils}}{2 \text{ students}}\), which is the original ratio, or by 4 gives \(\frac{2 \times 4}{1 \times 4} = \frac{8 \text{ pencils}}{4 \text{ students}}\).
Step 4: Compare each given option to the simplified ratio \(\frac{2 \text{ pencils}}{1 \text{ student}}\) or the original ratio \(\frac{4 \text{ pencils}}{2 \text{ students}}\) to see if they represent the same relationship.
Step 5: Conclude that any ratio that can be simplified or scaled to \(\frac{2 \text{ pencils}}{1 \text{ student}}\) or \(\frac{4 \text{ pencils}}{2 \text{ students}}\) is equivalent to the original ratio.
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