Mark and Anson each have a video game collection.
The number of video games in Mark collection can be represented by x.
The number of video games in Anson collection is 5 times the number in Mark collection.
The total number of video games is no more than 72.
What is the solution set for x, the number of video games in Mark's collection?
x less than or equal to 12
x is less then or equal to -12
x is greater than or equal to 15
x is greater than or equal to -1
5 answers
The correct solution set for x is x less than or equal to 12
can you show the process and explain
Certainly! Let's break down the problem step by step:
1. Let's represent the number of video games in Mark's collection as x.
2. The number of video games in Anson's collection is 5 times the number in Mark's collection, so we can express it as 5x.
3. The total number of video games is the sum of Mark's and Anson's collections, which is x + 5x.
4. The problem states that the total number of video games is no more than 72, so we can write the inequality as:
x + 5x ≤ 72
5. Simplifying the inequality, we get:
6x ≤ 72
x ≤ 72/6
x ≤ 12
6. So, the solution set for x, the number of video games in Mark's collection, is x ≤ 12.
This means that Mark can have any number of video games less than or equal to 12 in his collection. For example, he could have 10 video games, 5 video games, or even no video games (0).
1. Let's represent the number of video games in Mark's collection as x.
2. The number of video games in Anson's collection is 5 times the number in Mark's collection, so we can express it as 5x.
3. The total number of video games is the sum of Mark's and Anson's collections, which is x + 5x.
4. The problem states that the total number of video games is no more than 72, so we can write the inequality as:
x + 5x ≤ 72
5. Simplifying the inequality, we get:
6x ≤ 72
x ≤ 72/6
x ≤ 12
6. So, the solution set for x, the number of video games in Mark's collection, is x ≤ 12.
This means that Mark can have any number of video games less than or equal to 12 in his collection. For example, he could have 10 video games, 5 video games, or even no video games (0).
can you literally show me the math you did
Certainly! Here is the step-by-step breakdown of the math:
1. We represent the number of video games in Mark's collection as x.
2. The number of video games in Anson's collection is 5 times the number in Mark's collection, so Anson's collection can be represented as 5x.
3. The total number of video games is the sum of Mark's and Anson's collections, which can be expressed as x + 5x.
4. The problem states that the total number of video games is no more than 72, so we can write the inequality as x + 5x ≤ 72.
To solve this inequality:
5. Combine like terms: x + 5x = 6x.
6. Rewrite the inequality: 6x ≤ 72.
7. Divide both sides of the inequality by 6 to isolate x: (6x)/6 ≤ 72/6.
8. Simplify: x ≤ 12.
Therefore, the solution set for x, the number of video games in Mark's collection, is x ≤ 12.
1. We represent the number of video games in Mark's collection as x.
2. The number of video games in Anson's collection is 5 times the number in Mark's collection, so Anson's collection can be represented as 5x.
3. The total number of video games is the sum of Mark's and Anson's collections, which can be expressed as x + 5x.
4. The problem states that the total number of video games is no more than 72, so we can write the inequality as x + 5x ≤ 72.
To solve this inequality:
5. Combine like terms: x + 5x = 6x.
6. Rewrite the inequality: 6x ≤ 72.
7. Divide both sides of the inequality by 6 to isolate x: (6x)/6 ≤ 72/6.
8. Simplify: x ≤ 12.
Therefore, the solution set for x, the number of video games in Mark's collection, is x ≤ 12.
1 answer