**Answer: A:3 rolls B: $38.67**

**Step-by-step explanation: **

**1. Convert all units to the same value (feet to inches, as the opposite gives fractions)**

**2. Use new equation and multiply the said new variable (84*3 & 96*3)**

**3. The new total should amount to the total area (540)**

**4. Divide found area by 12 to convert back into feet (45)**

**5. Divide the feet by feet per roll (3)**

**6. Multiply for Cost**

**Answer:**

No solutions.

**General Formulas and Concepts:**

<u>Pre-Algebra</u>

- Order of Operations:
**BPEMDAS** - Equality Properties

<u>Algebra I</u>

- Solving systems of equations using substitution/elimination
- Solving systems of equations by graphing
- Expanding
- Finding roots of a quadratic
- Standard Form:
**ax² + bx + c = 0** - Quadratic Formula:

**Step-by-step explanation:**

<u>Step 1: Define systems</u>

2x - y = 9

4x² + 3y² - 2x + y = 16

<u>Step 2: Rewrite systems</u>

2x - y = 9

- Subtract 2x on both sides: -y = 9 - 2x
- Divide -1 on both sides: y = 2x - 9

<u>Step 3: Redefine systems</u>

y = 2x - 9

4x² + 3y² - 2x + y = 16

<u>Step 4: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

- Substitute in <em>y</em>: 4x² + 3(2x - 9)² - 2x + (2x - 9) = 16
- Expand: 4x² + 3(4x² - 36x + 81) - 2x + (2x - 9) = 16
- Distribute 3: 4x² + 12x² - 108x + 243 - 2x + 2x - 9 = 16
- Combine like terms: 16x² - 108x + 234 = 16
- Factor GCF: 2(8x² - 54x + 117) = 16
- Divide 2 on both sides: 8x² - 54x + 117 = 8
- Subtract 8 on both sides: 8x² - 54x + 109 = 0
- Define variables: a = 8, b = -54, c = 109
- Resubstitute:
- Exponents:
- Multiply:
- Subtract:

Here we see that we start to delve into imaginary roots. Since on a real number plane, we do not have imaginary roots, there would be no solution to the systems of equations.

<u>Step 5: Graph systems</u>

<em>We can verify our results.</em>

Rate is distance/time

320 miles in 8 hours

320=distance

8=time

320/8=rate=40miles per hour

230=distance

5=time

230/5=rate=46 miles per hour

46>40

46-40=6

maruce faster by 6 miles per hour

**Answer:**

**Step-by-step explanation:**

There's a calculated explanation below. I hope this helps!