1. **Stating the problem:** We have two fraction equations to solve for $x$: Equation 1: $\frac{234}{x} - \frac{45}{100} = ?$ with $x=520$ given. Equation 2: $\frac{58}{x} = \frac{80}{100}$ with $x=72.5$ given. 2. **Equation 1:** $\frac{234}{x} - \frac{45}{100}$ with $x=520$. Substitute $x=520$: $$\frac{234}{520} - \frac{45}{100}$$ Simplify each fraction: $$\frac{234}{520} = \frac{\cancel{234}}{\cancel{520}} = \frac{117}{260}$$ (dividing numerator and denominator by 2) $$\frac{45}{100} = \frac{9}{20}$$ (dividing numerator and denominator by 5) Find common denominator for $\frac{117}{260}$ and $\frac{9}{20}$: LCM of 260 and 20 is 260. Convert $\frac{9}{20}$ to denominator 260: $$\frac{9}{20} = \frac{9 \times 13}{20 \times 13} = \frac{117}{260}$$ So: $$\frac{117}{260} - \frac{117}{260} = 0$$ 3. **Equation 2:** $\frac{58}{x} = \frac{80}{100}$ with $x=72.5$. Substitute $x=72.5$: $$\frac{58}{72.5} = \frac{80}{100}$$ Simplify right side: $$\frac{80}{100} = \frac{4}{5}$$ Calculate left side: $$\frac{58}{72.5} = 0.8$$ Calculate right side: $$\frac{4}{5} = 0.8$$ Both sides equal 0.8, so $x=72.5$ satisfies the equation. **Final answers:** Equation 1 evaluates to 0 when $x=520$. Equation 2 is true when $x=72.5$.