A cereal mixture contains wheat and corn. If `3.5` kg of cereal has 2 kg of wheat, how much wheat will be there in `5.6` kg of cereal ?

Answer

To solve the problem step by step, we will use the information provided about the ratio of wheat to the total cereal mixture.

### Step 1: Determine the ratio of wheat in the cereal mixture.
We know that 3.5 kg of cereal contains 2 kg of wheat. Therefore, the ratio of wheat to cereal is:

\[ \text{Ratio of wheat} = \frac{\text{Weight of wheat}}{\text{Total weight of cereal}} = \frac{2 \text{ kg}}{3.5 \text{ kg}} \]

### Step 2: Calculate the amount of wheat per kg of cereal.
To find out how much wheat is in 1 kg of cereal, we divide the weight of wheat by the total weight of cereal:

\[ \text{Wheat per kg of cereal} = \frac{2 \text{ kg}}{3.5 \text{ kg}} = \frac{2}{3.5} = \frac{2 \times 10}{35} = \frac{20}{35} = \frac{4}{7} \text{ kg of wheat per kg of cereal} \]

### Step 3: Calculate the amount of wheat in 5.6 kg of cereal.
Now, we need to find out how much wheat is in 5.6 kg of cereal. We can use the ratio we calculated in Step 2:

\[ \text{Wheat in 5.6 kg of cereal} = \left(\frac{4}{7} \text{ kg of wheat per kg of cereal}\right) \times 5.6 \text{ kg of cereal} \]

### Step 4: Perform the multiplication.
Calculating the amount of wheat:

\[ \text{Wheat in 5.6 kg} = \frac{4}{7} \times 5.6 = \frac{4 \times 5.6}{7} \]

To make the calculation easier, we can convert 5.6 into a fraction:

\[ 5.6 = \frac{56}{10} = \frac{28}{5} \]

Now substituting this into our equation:

\[ \text{Wheat in 5.6 kg} = \frac{4}{7} \times \frac{28}{5} = \frac{4 \times 28}{7 \times 5} = \frac{112}{35} \]

### Step 5: Simplify the fraction.
Now we simplify \(\frac{112}{35}\):

\[ \frac{112 \div 7}{35 \div 7} = \frac{16}{5} \]

### Step 6: Convert to decimal.
Finally, we can convert \(\frac{16}{5}\) into a decimal:

\[ \frac{16}{5} = 3.2 \]

### Conclusion:
Thus, the amount of wheat in 5.6 kg of cereal is **3.2 kg**.

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