To calculate how many eggs Jaden's family had left after selling some cartons, we need to follow these steps:
Step 1: Calculate the total number of eggs they brought.
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Brown eggs:
- They brought 37 cartons of brown eggs.
- Each carton holds 12 eggs. \[ \text{Total brown eggs} = 37 \text{ cartons} \times 12 \text{ eggs/carton} = 444 \text{ brown eggs} \]
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White eggs:
- They brought 61 cartons of white eggs.
- Each carton holds 6 eggs. \[ \text{Total white eggs} = 61 \text{ cartons} \times 6 \text{ eggs/carton} = 366 \text{ white eggs} \]
Step 2: Calculate the total number of eggs they sold.
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Brown eggs sold:
- They sold 29 cartons of brown eggs. \[ \text{Brown eggs sold} = 29 \text{ cartons} \times 12 \text{ eggs/carton} = 348 \text{ brown eggs} \]
-
White eggs sold:
- They sold 56 cartons of white eggs. \[ \text{White eggs sold} = 56 \text{ cartons} \times 6 \text{ eggs/carton} = 336 \text{ white eggs} \]
Step 3: Calculate the remaining eggs.
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Brown eggs left: \[ \text{Brown eggs left} = \text{Total brown eggs} - \text{Brown eggs sold} = 444 - 348 = 96 \text{ brown eggs} \]
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White eggs left: \[ \text{White eggs left} = \text{Total white eggs} - \text{White eggs sold} = 366 - 336 = 30 \text{ white eggs} \]
Step 4: Calculate the total number of eggs left. \[ \text{Total eggs left} = \text{Brown eggs left} + \text{White eggs left} = 96 + 30 = 126 \text{ eggs} \]
Therefore, the total number of eggs they had left is \( \boxed{126} \).