Sure, let's go through the solution step-by-step.
### Step 1: Understand the Problem
We know that one cake requires:
- [tex]\( \frac{1}{2} \)[/tex] kg of flour
- [tex]\( \frac{2}{3} \)[/tex] kg of sugar
We want to find out how much flour and sugar is needed to make 4 dozen (i.e., 48) cakes.
### Step 2: Determine the Total Number of Cakes
Since 1 dozen consists of 12 cakes, 4 dozens would be:
[tex]\[
4 \times 12 = 48 \text{ cakes}
\][/tex]
### Step 3: Calculate the Total Amount of Flour Needed
One cake needs [tex]\( \frac{1}{2} \)[/tex] kg of flour. Therefore, for 48 cakes, the total amount of flour needed is:
[tex]\[
48 \times \frac{1}{2} = 24 \text{ kg of flour}
\][/tex]
### Step 4: Calculate the Total Amount of Sugar Needed
One cake needs [tex]\( \frac{2}{3} \)[/tex] kg of sugar. Therefore, for 48 cakes, the total amount of sugar needed is:
[tex]\[
48 \times \frac{2}{3} = 32 \text{ kg of sugar}
\][/tex]
### Conclusion
To make 4 dozens (48) cakes, Tom will need:
- 24 kg of flour
- 32 kg of sugar
Thus, the complete solution is:
[tex]\[
\text{Total cakes:}\ 48 \text{ cakes}
\][/tex]
[tex]\[
\text{Total flour needed:}\ 24 \text{ kg}
\][/tex]
[tex]\[
\text{Total sugar needed:}\ 32 \text{ kg}
\][/tex]
