season Levala scored 6 more goals than Mary. Use ratios to compare the number of goals scored by Mary and Lerato in each of the following situations: a) Lerato scored 42 goals. b) Mary scored 18 goals.

To compare the number of goals scored by Mary and Lerato using ratios, let's analyze each situation step-by-step. ### Given: - **Lerato scored 6 more goals than Mary.** Mathematically, this can be expressed as: \[ \text{Lerato's Goals} = \text{Mary's Goals} + 6 \] ### a) **Lerato scored 42 goals.** 1. **Determine Mary's Goals:** \[ \text{Mary's Goals} = \text{Lerato's Goals} - 6 = 42 - 6 = 36 \] 2. **Form the Ratio (Mary : Lerato):** \[ 36 : 42 \] 3. **Simplify the Ratio:** - Find the greatest common divisor (GCD) of 36 and 42, which is 6. - Divide both parts of the ratio by 6: \[ \frac{36}{6} : \frac{42}{6} = 6 : 7 \] **Final Ratio:** \[ \text{Mary} : \text{Lerato} = 6 : 7 \] ### b) **Mary scored 18 goals.** 1. **Determine Lerato's Goals:** \[ \text{Lerato's Goals} = \text{Mary's Goals} + 6 = 18 + 6 = 24 \] 2. **Form the Ratio (Mary : Lerato):** \[ 18 : 24 \] 3. **Simplify the Ratio:** - Find the GCD of 18 and 24, which is 6. - Divide both parts of the ratio by 6: \[ \frac{18}{6} : \frac{24}{6} = 3 : 4 \] **Final Ratio:** \[ \text{Mary} : \text{Lerato} = 3 : 4 \] ### **Summary:** - **a) Lerato scored 42 goals:** **Mary : Lerato = 6 : 7** - **b) Mary scored 18 goals:** **Mary : Lerato = 3 : 4**