Modeling with Expressions - Pre Algebra

1. Pencils cost $p$ dollars each. What expression gives the total cost of 12 pencils and a 3 dollar notebook?

   $12p + 3$ dollars.

2. What expression gives the number of hours in $m$ minutes?

   $\frac{m}{60}$ hours, since 60 minutes make 1 hour.

3. A phone battery is at 80 percent and drops 5 percent per hour. What expression gives the battery level after $h$ hours?

   $80 - 5h$ percent.

4. A garden's length is 5 feet more than three times its width $w$. What expression gives its perimeter in feet?

   $8w + 10$. $2(3w + 5) + 2w = 6w + 10 + 2w$.

5. Why must $s$ be a whole number in a model where $s$ is the number of students?

   A fraction of a student is not possible, so the context limits $s$ to whole numbers.

6. In the term $12s$, 12 is in dollars per student and $s$ is a number of students. What unit does $12s$ have?

   Dollars. The unit "students" cancels: (dollars per student) times students gives dollars.

7. A car travels at 60 miles per hour for $t$ hours. What expression gives the distance traveled?

   $60t$ miles. Distance equals rate times time.

8. A rectangle has area $A$ square meters and width 4 meters. What expression gives its length?

   $\frac{A}{4}$ meters, since length equals area divided by width.

9. A museum trip costs 150 dollars for the bus plus 12 dollars per student. What expression gives the total cost for $s$ students?

   $150 + 12s$ dollars.

10. Small boxes hold 4 muffins and large boxes hold 10. What expression gives the muffins in $s$ small and $l$ large boxes?

    $4s + 10l$.

11. What expression gives the number of inches in $f$ feet?

    $12f$ inches, since each foot is 12 inches.

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