1. **State the problem:** We are given two purchases with amounts of trail mix and jelly beans and their total costs. We want to find the cost per pound of trail mix ($x$) and jelly beans ($y$). 2. **Write the system of equations:** From the table: $$3x + 5y = 23$$ $$6x + 2y = 20$$ 3. **Solve the system using substitution or elimination:** - Multiply the first equation by 2: $$2(3x + 5y) = 2(23) \Rightarrow 6x + 10y = 46$$ - Subtract the second equation from this: $$(6x + 10y) - (6x + 2y) = 46 - 20$$ $$6x - 6x + 10y - 2y = 26$$ $$8y = 26$$ $$y = \frac{26}{8} = 3.25$$ 4. **Find $x$ by substituting $y$ back into the first equation:** $$3x + 5(3.25) = 23$$ $$3x + 16.25 = 23$$ $$3x = 23 - 16.25 = 6.75$$ $$x = \frac{6.75}{3} = 2.25$$ 5. **Interpret the results:** - Cost per pound of trail mix ($x$) is 2.25 dollars. - Cost per pound of jelly beans ($y$) is 3.25 dollars. **Final answer:** - Trail mix costs $2.25$ per pound. - Jelly beans cost $3.25$ per pound.