1. **Problem statement:** Jack's and Angie's savings are in the ratio 21 : 8, and Angie's and Hazel's savings are in the ratio 4 : 9. The total savings of Jack, Angie, and Hazel is 94. We need to find how much more savings Jack has than Hazel. 2. **Step 1: Express the ratios with variables.** Let Jack's savings = $21x$, Angie's savings = $8x$ (from the first ratio). 3. **Step 2: Use the second ratio for Angie and Hazel.** Angie's savings : Hazel's savings = 4 : 9. Since Angie's savings is $8x$, set $8x = 4y$ to find Hazel's savings in terms of $x$. 4. **Step 3: Solve for $y$.** $8x = 4y \implies y = 2x$. 5. **Step 4: Find Hazel's savings.** Hazel's savings = $9y = 9 \times 2x = 18x$. 6. **Step 5: Write the total savings equation.** Jack + Angie + Hazel = $21x + 8x + 18x = 47x = 94$. 7. **Step 6: Solve for $x$.** $47x = 94 \implies x = \frac{94}{47} = 2$. 8. **Step 7: Calculate Jack's and Hazel's savings.** Jack's savings = $21x = 21 \times 2 = 42$. Hazel's savings = $18x = 18 \times 2 = 36$. 9. **Step 8: Find how much more Jack has than Hazel.** Difference = $42 - 36 = 6$. **Final answer:** Jack has 6 more savings than Hazel.