List the set that satisfies the given condition: A positive multiple of 3 and less than 16.
$\ldots,-6,-3,0,3,6,9 \ldots$
${3,6,9,12,15}$
${3,6,9,12,15,18 \ldots}$
${1,2,3, \ldots 16}$
Answer (2)
List positive multiples of 3.
Identify multiples of 3 that are less than 16.
Form the set containing these multiples.
The set that satisfies the condition is 3 , 6 , 9 , 12 , 15 .
Explanation
Understanding the Problem We need to find the set of numbers that are positive multiples of 3 and less than 16. This means we are looking for numbers that can be obtained by multiplying 3 by a positive integer, and the result must be smaller than 16.
Listing Multiples of 3 Let's list the positive multiples of 3:
3 × 1 = 3 3 × 2 = 6 3 × 3 = 9 3 × 4 = 12 3 × 5 = 15 3 × 6 = 18
We stop here because 3 × 6 = 18 which is greater than 16.
Identifying Numbers Less Than 16 Now, we select the multiples of 3 that are less than 16. From the list above, these are 3, 6, 9, 12, and 15.
Final Set Therefore, the set that satisfies the condition is {3, 6, 9, 12, 15}.
Final Answer The correct answer is the set {3, 6, 9, 12, 15}.
Examples
Understanding multiples and constraints is crucial in many real-life scenarios. For example, if you're planning a party and need to buy snacks that come in packs of 3, and you only want to spend up to $16, you need to determine how many packs you can buy. If each pack costs $1, then you can buy 1, 2, 3, 4, or 5 packs, corresponding to spending $3, $6, $9, $12, or $15. This problem demonstrates how identifying multiples within a certain limit helps in making purchasing decisions.
The set that consists of positive multiples of 3 and is less than 16 is {3, 6, 9, 12, 15}.
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