1. **Problem statement:** We are given quantities of hair colour, colour developer, conditioner, and thickener, and we need to find and simplify ratios as fractions. 2. **Recall:** A ratio compares two quantities and can be expressed as a fraction. To simplify, divide numerator and denominator by their greatest common divisor (GCD). 3. **Part a:** Ratio of hair colour to thickener. Given: hair colour = 20 mL, thickener = 3 mL. Ratio = $\frac{20}{3}$. Since 20 and 3 have no common factors other than 1, the ratio in simplest form is $\frac{20}{3}$. 4. **Part b:** Ratio of thickener to conditioner. Given: thickener = 3 mL, conditioner = 15 mL. Ratio = $\frac{3}{15}$. Simplify by dividing numerator and denominator by 3: $$\frac{\cancel{3}}{\cancel{15}} = \frac{1}{5}$$ 5. **Part c:** Ratio of customer price to actual cost. Given: customer price = 68, actual cost = 14.20. Express 14.20 as fraction: $14.20 = \frac{1420}{100}$. Ratio = $\frac{68}{14.20} = \frac{68}{\frac{1420}{100}} = 68 \times \frac{100}{1420} = \frac{6800}{1420}$. Simplify numerator and denominator by dividing by 20: $$\frac{\cancel{6800}^{340}}{\cancel{1420}^{71}} = \frac{340}{71}$$ 340 and 71 share no common factors other than 1, so ratio in simplest form is $\frac{340}{71}$. **Final answers:** a. $\frac{20}{3}$ b. $\frac{1}{5}$ c. $\frac{340}{71}$