8-26-24 Mastering Equations and Formulas

Answer explanation

The correct equation is C = 50 + 0.20m because the total cost includes a flat fee of 50 plus 0.20 per mile driven.

Solve the following real-world equation: If a person earns $15 per hour and works h hours, their total earnings E are given by E = 15h. How many hours did they work if they earned $300?

Answer explanation

To find the number of hours worked, we need to solve the equation E = 15h where E = $300. Substituting E = $300, we get 300 = 15h. Solving for h, we find h = 20. Therefore, the person worked 20 hours.

Evaluate the data from the word problem: A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 units, what is the width of the rectangle?

Answer explanation

Since the length is 3 times the width, let the width be x. Therefore, the length is 3x. Perimeter = 2(length + width). Substituting the values and solving the equation gives x = 6 units.

Answer explanation

To solve for w, isolate w on one side of the equation. Start by subtracting 2l from both sides to get P - 2l = 2w. Then, divide by 2 to solve for w, giving w = (P - 2l) / 2.

Answer explanation

To solve the linear equation, first, combine like terms by subtracting 2x from both sides to get 3x - 3 = 9. Then, add 3 to both sides to isolate x, resulting in x = 4. Therefore, the correct answer is x = 4.

Answer explanation

To solve the equation, first distribute the 3 on the left side: 3x - 6 + 4 = 2x + 6. Combine like terms to get x = 4.

• x = {4, -4}

• x = {-1, 4}

• x = {1, -4}

• x = {1, -1}

Answer explanation

To solve the equation, first isolate the absolute value term by dividing both sides by 3. Then, split the equation into two cases: 2x + 3 = 15 and 2x + 3 = -15. Solve for x in each case to get x = 1 and x = -4. Therefore, x = {1, -4}.

Answer explanation

To solve for w, divide both sides of the formula V = lwh by lh. This gives w = V / lh, which is the correct rearranged formula.