1. **State the problem:** Joanie has 50.75 dollars and buys three items: a burger, a souvenir, and a pass. The burger costs $\frac{1}{6}$ as much as the souvenir, and the souvenir costs $\frac{3}{4}$ the cost of the pass. After buying these, she has 2.00 dollars left. We need to find the cost of each item. 2. **Define variables:** Let $p$ be the cost of the pass. Then the souvenir costs $s = \frac{3}{4}p$. The burger costs $b = \frac{1}{6}s = \frac{1}{6} \times \frac{3}{4}p = \frac{3}{24}p = \frac{1}{8}p$. 3. **Write the total cost equation:** Total money - leftover = sum of costs \[ 50.75 - 2.00 = b + s + p \] \[ 48.75 = b + s + p \] Substitute $b$ and $s$: \[ 48.75 = \frac{1}{8}p + \frac{3}{4}p + p \] 4. **Combine like terms:** Find common denominator 8: \[ \frac{1}{8}p + \frac{6}{8}p + \frac{8}{8}p = \frac{1+6+8}{8}p = \frac{15}{8}p \] So: \[ 48.75 = \frac{15}{8}p \] 5. **Solve for $p$:** Multiply both sides by $\frac{8}{15}$: \[ p = 48.75 \times \frac{8}{15} \] Calculate: \[ p = 48.75 \times \frac{8}{15} = 48.75 \times 0.5333... = 26 \] 6. **Find $s$ and $b$:** \[ s = \frac{3}{4}p = \frac{3}{4} \times 26 = 19.5 \] \[ b = \frac{1}{8}p = \frac{1}{8} \times 26 = 3.25 \] 7. **Check the sum:** \[ 3.25 + 19.5 + 26 = 48.75 \] Add leftover 2.00: \[ 48.75 + 2.00 = 50.75 \] Matches the total money Joanie had. **Final answer:** - Burger cost: \$3.25 - Souvenir cost: \$19.50 - Pass cost: \$26.00