This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Another one danielalheri09@gmail.com — let's solve it. Step 1: Understand the problem. Sarah and Sarat have a total of 12 marbles. We need to find all possible ways they could share these marbles, meaning we need to find pairs of numbers that add up to 12. Step 2: List the possible combinations. Let S be the number of marbles Sarah has and R be the number of marbles Sarat has. We know that S + R = 12. We will list all non-negative integer pairs (S, R) that satisfy this equation. • If Sarah has 0 marbles, Sarat has 12 - 0 = 12 marbles. (0, 12) • If Sarah has 1 marble, Sarat has 12 - 1 = 11 marbles. (1, 11) • If Sarah has 2 marbles, Sarat has 12 - 2 = 10 marbles. (2, 10) • If Sarah has 3 marbles, Sarat has 12 - 3 = 9 marbles. (3, 9) • If Sarah has 4 marbles, Sarat has 12 - 4 = 8 marbles. (4, 8) • If Sarah has 5 marbles, Sarat has 12 - 5 = 7 marbles. (5, 7) • If Sarah has 6 marbles, Sarat has 12 - 6 = 6 marbles. (6, 6) • If Sarah has 7 marbles, Sarat has 12 - 7 = 5 marbles. (7, 5) • If Sarah has 8 marbles, Sarat has 12 - 8 = 4 marbles. (8, 4) • If Sarah has 9 marbles, Sarat has 12 - 9 = 3 marbles. (9, 3) • If Sarah has 10 marbles, Sarat has 12 - 10 = 2 marbles. (10, 2) • If Sarah has 11 marbles, Sarat has 12 - 11 = 1 marble. (11, 1) • If Sarah has 12 marbles, Sarat has 12 - 12 = 0 marbles. (12, 0) Step 3: State all possible distributions. The possible numbers of marbles they could have each are: (0, 12), (1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6), (7, 5), (8, 4), (9, 3), (10, 2), (11, 1), (12, 0) The possible ways they could have marbles are: Sarah could have 0 and Sarat 12. Sarah could have 1 and Sarat 11. Sarah could have 2 and Sarat 10. Sarah could have 3 and Sarat 9. Sarah could have 4 and Sarat 8. Sarah could have 5 and Sarat 7. Sarah could have 6 and Sarat 6. Sarah could have 7 and Sarat 5. Sarah could have 8 and Sarat 4. Sarah could have 9 and Sarat 3. Sarah could have 10 and Sarat 2. Sarah could have 11 and Sarat 1. Sarah could have 12 and Sarat 0. These are all the possible distributions. What's next? 📸