To determine whether the ratio table has been set up correctly, we need to analyze the given information.
The table provided is:
Cartons 1 2 3 4 5
Eggs 12 24 36 48 60
We know that each carton contains 12 eggs. Therefore, we can calculate the number of eggs for each number of cartons:
- For 1 carton: \(1 \times 12 = 12\)
- For 2 cartons: \(2 \times 12 = 24\)
- For 3 cartons: \(3 \times 12 = 36\)
- For 4 cartons: \(4 \times 12 = 48\)
- For 5 cartons: \(5 \times 12 = 60\)
All the values in the table are correct, as they correspond to the number of eggs based on the number of cartons.
Now, let's check the ratios:
The ratio of eggs to cartons can be expressed as:
For 1 carton: \( \frac{12}{1} = 12 \) (which simplifies to \( \frac{12}{1} \)) For 2 cartons: \( \frac{24}{2} = 12 \) (which simplifies to \( \frac{12}{1} \)) For 3 cartons: \( \frac{36}{3} = 12 \) (which simplifies to \( \frac{12}{1} \)) For 4 cartons: \( \frac{48}{4} = 12 \) (which simplifies to \( \frac{12}{1} \)) For 5 cartons: \( \frac{60}{5} = 12 \) (which simplifies to \( \frac{12}{1} \))
Since every ratio simplifies to \( \frac{12}{1} \), the table is set up correctly, and we can conclude that:
The table has been set up correctly because all ratios in the table simplify to \( \frac{12}{1} \).