1. **State the problem:** We are given quantities of hair colour, colour developer, conditioner, and thickener, and we need to find and simplify certain ratios as fractions. 2. **Ratios to find:** a. Hair colour to thickener b. Thickener to conditioner c. Customer price to actual cost 3. **Recall:** A ratio $a:b$ can be expressed as the fraction $\frac{a}{b}$ and simplified by dividing numerator and denominator by their greatest common divisor (GCD). 4. **Calculate each ratio:** a. Hair colour to thickener = $\frac{20}{3}$ - GCD of 20 and 3 is 1, so ratio in lowest terms is $\frac{20}{3}$. b. Thickener to conditioner = $\frac{3}{15}$ - GCD of 3 and 15 is 3. - Simplify: $$\frac{\cancel{3}}{\cancel{15}} = \frac{1}{5}$$ c. Customer price to actual cost = $\frac{68.00}{14.20}$ - Convert to whole numbers by multiplying numerator and denominator by 100: $$\frac{68.00 \times 100}{14.20 \times 100} = \frac{6800}{1420}$$ - GCD of 6800 and 1420 is 20. - Simplify: $$\frac{\cancel{6800}^{340}}{\cancel{1420}^{71}} = \frac{340}{71}$$ 5. **Final answers:** a. $\frac{20}{3}$ b. $\frac{1}{5}$ c. $\frac{340}{71}$