Representing Constraints - Pre Algebra

1. A trip needs at least 20 students to run. Which inequality represents this for $s$ students?

   $s \ge 20$.

2. Adult tickets cost 10 dollars and student tickets cost 6 dollars. A group must spend exactly 120 dollars. Which equation represents this?

   $10a + 6s = 120$, where $a$ is adult tickets and $s$ is student tickets.

3. In $10a + 6s = 120$, with tickets at 10 and 6 dollars, what does the term $6s$ represent?

   The total amount spent on student tickets, in dollars.

4. Which inequality symbol represents "must not exceed" in a constraint?

   $\le$. The quantity can equal the limit or be less.

5. A van holds at most 1500 pounds. The driver and gear weigh 300 pounds, and each box weighs 40 pounds. Which inequality limits the boxes $b$?

   $300 + 40b \le 1500$.

6. In $300 + 40b \le 1500$ for a van's load in pounds, what does 1500 represent?

   The maximum total weight allowed, in pounds.

7. A tank starts with 90 gallons and loses 6 gallons per minute. It must keep at least 30 gallons. Which inequality limits the minutes $t$?

   $90 - 6t \ge 30$.

8. A rectangle's length $l$ must be at least 3 feet more than its width $w$. Which inequality represents this?

   $l \ge w + 3$.

9. A bag holds at most 15 pounds. A laptop weighs 3 pounds and each book weighs 2 pounds. Which inequality limits the books $b$?

   $2b + 3 \le 15$.

10. Which inequality symbol represents "a minimum of" in a constraint?

    $\ge$. The quantity can equal the minimum or be greater.

11. A rectangle must have a perimeter of exactly 60 feet. Which equation in $l$ and $w$ represents this?

    $2l + 2w = 60$.

12. When should a constraint be written as an equation rather than an inequality?

    When the quantity must equal one exact value, such as a fixed total, rather than stay within a limit.

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