1. **State the problem:** Tamika and Kevin each work two part-time jobs mowing lawns and raking yards. Tamika earns 10 per lawn and 5 per yard, wants to earn more than 200. Kevin earns 12 per lawn and 3 per yard, wants to earn more than 180. 2. **Write the system of inequalities:** Let $x$ be the number of lawns mowed and $y$ be the number of yards raked (same for both). Tamika's earnings: $$10x + 5y > 200$$ Kevin's earnings: $$12x + 3y > 180$$ 3. **Given conditions:** - They mowed the same number of lawns and raked the same number of yards. - Kevin met his goal: $$12x + 3y > 180$$ - Tamika did not meet her goal: $$10x + 5y \leq 200$$ 4. **Find a possible combination $(x,y)$:** From Kevin's inequality: $$12x + 3y > 180$$ Divide both sides by 3: $$\cancel{3}(4x + y) > \cancel{3}60$$ $$4x + y > 60$$ From Tamika's inequality: $$10x + 5y \leq 200$$ Divide both sides by 5: $$\cancel{5}(2x + y) \leq \cancel{5}40$$ $$2x + y \leq 40$$ 5. **Choose $x$ and $y$ satisfying both:** Try $x=10$ lawns. Kevin: $$4(10) + y > 60 \Rightarrow 40 + y > 60 \Rightarrow y > 20$$ Tamika: $$2(10) + y \leq 40 \Rightarrow 20 + y \leq 40 \Rightarrow y \leq 20$$ No $y$ satisfies both $y > 20$ and $y \leq 20$ simultaneously. Try $x=11$ lawns. Kevin: $$4(11) + y > 60 \Rightarrow 44 + y > 60 \Rightarrow y > 16$$ Tamika: $$2(11) + y \leq 40 \Rightarrow 22 + y \leq 40 \Rightarrow y \leq 18$$ So $y$ must satisfy $16 < y \leq 18$. Choose $y=17$ yards. 6. **Check earnings:** Tamika: $$10(11) + 5(17) = 110 + 85 = 195 \leq 200$$ (did not meet goal) Kevin: $$12(11) + 3(17) = 132 + 51 = 183 > 180$$ (met goal) **Answer:** A possible combination is $x=11$ lawns and $y=17$ yards.