Answer:
[tex]x=70[/tex]
General Formulas and Concepts:
Pre-Alg
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
Step 1: Define equation
[tex]\frac{0.35}{\frac{2}{3}x } =\frac{0.45}{x-10}[/tex]
Step 2: Solve for x
- Cross-multiply: [tex]0.35(x-10)=\frac{2}{3} x \cdot 0.45[/tex]
- Distribute 0.35: [tex]0.35x - 3.5=\frac{2}{3} x \cdot 0.45[/tex]
- Multiply: [tex]0.35x - 3.5=0.3x[/tex]
- Isolate x term: [tex]-3.5=-0.05x[/tex]
- Isolate x: [tex]70=x[/tex]
- Rewrite: [tex]x=70[/tex]
Step 3: Check
Plug in x to verify it's a solution.
- Substitute: [tex]\frac{0.35}{\frac{2}{3}(70) } =\frac{0.45}{70-10}[/tex]
- Multiply: [tex]\frac{0.35}{\frac{140}{3} } =\frac{0.45}{70-10}[/tex]
- Subtract: [tex]\frac{0.35}{\frac{140}{3} } =\frac{0.45}{60}[/tex]
- Evaluate: [tex]0.0075=0.0075[/tex]
