Mastering Literal Equations: Constants, Coefficients, & Solving

1. A rectangle has a length represented by L and a width represented by W. The area A of the rectangle can be expressed as A = L * W. If the area is 48 square units and the width is 4 units, what is the length of the rectangle? Identify the constant and coefficient in the equation.

• 8 units

• 16 units

• 12 units

• 10 units

2. The formula for the perimeter P of a triangle is P = a + b + c, where a, b, and c are the lengths of the sides. If the perimeter is 30 units and two sides are 10 units and 8 units, what is the length of the third side? Apply properties of equality to solve for c.

• 10

• 12

• 15

• 8

3. The formula for the total cost C of a meal is C = m + t, where m is the meal cost and t is the tip. If the total cost is $50 and the tip is 15% of the meal cost, express the meal cost in terms of C and t, and find the meal cost.

• 45.00

• 43.48

• 50.00

• 40.00

4. The distance D traveled by a car can be expressed as D = rt, where r is the rate of speed and t is the time traveled. If a car travels for 3 hours at a speed of 60 miles per hour, what is the distance traveled? Identify the constants and coefficients in the equation.

• 150 miles

• 200 miles

• 120 miles

• 180 miles

5. The formula for the volume V of a cylinder is V = πr²h, where r is the radius and h is the height. If the volume is 100π cubic units and the height is 5 units, what is the radius of the cylinder? Use properties of equality to isolate r.

• 2π

• 2√5

• 4

• 3√5

6. The formula for the simple interest I earned on a loan is I = Prt, where P is the principal, r is the rate, and t is the time in years. If the interest earned is $200, the principal is $1000, and the time is 2 years, what is the rate of interest? Identify the constants and coefficients.

• 10%

• 20%

• 15%

• 5%

7. The formula for the speed S of an object is S = d/t, where d is the distance and t is the time. If an object travels 150 meters in 5 seconds, what is its speed? Identify the constants and coefficients in the equation.

• 30 meters per second

• 40 meters per second

• 35 meters per second

• 25 meters per second

8. The formula for the circumference C of a circle is C = 2πr. If the circumference is 31.4 units, what is the radius of the circle? Use properties of equality to solve for r and identify the constants and coefficients.

• 3.2

• 10.5

• 7.0

• 5.0

9. The formula for the total weight W of a shipment is W = n * w, where n is the number of items and w is the weight of each item. If the total weight is 120 pounds and each item weighs 5 pounds, how many items are in the shipment? Identify the constants and coefficients in the equation.

• 15

• 30

• 20

• 24

10. The formula for the final temperature T of a mixture is T = (T1 + T2)/2, where T1 and T2 are the temperatures of the two substances. If the final temperature is 70 degrees and one substance is at 60 degrees, what is the temperature of the other substance? Use properties of equality to solve for T2.

• 50 degrees

• 80 degrees

• 90 degrees

• 70 degrees