1. **State the problem:** We have four variables represented by emojis: 🍪 (cookie), 🍫 (chocolate), ☕ (mug), and 🍰 (cake). The system of equations is: $$\frac{🍪}{🍫} \times ☕ = 36$$ $$\frac{160}{🍪} = 8$$ $$🍫 \times 🍫 = 🍪 + 🍫$$ $$☕ - 🍰 = 6$$ We want to find the value of: $$🍪 + 🍰 \times ☕ - 🍫$$ 2. **Solve for each variable step-by-step:** - From the second equation: $$\frac{160}{🍪} = 8$$ Multiply both sides by $🍪$: $$160 = 8 \times 🍪$$ Divide both sides by 8: $$\cancel{8} \times \frac{160}{\cancel{8}} = \cancel{8} \times \frac{🍪}{\cancel{8}} \Rightarrow 20 = 🍪$$ So, $🍪 = 20$. - Substitute $🍪 = 20$ into the first equation: $$\frac{20}{🍫} \times ☕ = 36$$ Multiply both sides by $🍫$: $$20 \times ☕ = 36 \times 🍫$$ Rewrite as: $$20☕ = 36🍫$$ - From the third equation: $$🍫 \times 🍫 = 20 + 🍫$$ Rewrite as: $$🍫^2 = 20 + 🍫$$ Bring all terms to one side: $$🍫^2 - 🍫 - 20 = 0$$ - Solve quadratic equation for $🍫$: $$a=1, b=-1, c=-20$$ $$🍫 = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{1 \pm \sqrt{1 + 80}}{2} = \frac{1 \pm \sqrt{81}}{2} = \frac{1 \pm 9}{2}$$ Two solutions: $$🍫 = \frac{1 + 9}{2} = 5$$ $$🍫 = \frac{1 - 9}{2} = -4$$ Since $🍫$ represents a quantity, take $🍫 = 5$. - Substitute $🍫 = 5$ into the equation $20☕ = 36🍫$: $$20☕ = 36 \times 5 = 180$$ Divide both sides by 20: $$\cancel{20} \times \frac{☕}{\cancel{20}} = \frac{180}{20} \Rightarrow ☕ = 9$$ - From the fourth equation: $$☕ - 🍰 = 6$$ Substitute $☕ = 9$: $$9 - 🍰 = 6$$ Subtract 9 from both sides: $$-🍰 = 6 - 9 = -3$$ Multiply both sides by -1: $$🍰 = 3$$ 3. **Calculate the final expression:** $$🍪 + 🍰 \times ☕ - 🍫 = 20 + 3 \times 9 - 5$$ Calculate multiplication first: $$3 \times 9 = 27$$ So: $$20 + 27 - 5 = 42$$ **Final answer:** $$\boxed{42}$$