To divide 80 pence into two parts in the ratio [tex]\( 3:2 \)[/tex], let's go through the process step-by-step.
### Step 1: Understand the Ratio
The ratio [tex]\( 3:2 \)[/tex] means for every 5 parts (3 parts of one type and 2 parts of the other type), 3 parts will go to the first portion and 2 parts will go to the second portion.
### Step 2: Calculate the Total Parts
Add the parts of the ratio together to get the total number of parts:
[tex]\[ 3 + 2 = 5 \][/tex]
### Step 3: Determine the Value of One Part
To find out how much one part is worth, we divide the total amount (80 pence) by the total number of parts (5):
[tex]\[ \text{Value of one part} = \frac{80 \text{ pence}}{5} = 16 \text{ pence} \][/tex]
### Step 4: Calculate Each Portion
Now, we will allocate the value of one part to each portion according to the given ratio.
- First portion: The first portion has 3 parts.
[tex]\[ 3 \text{ parts} \times 16 \text{ pence per part} = 48 \text{ pence} \][/tex]
- Second portion: The second portion has 2 parts.
[tex]\[ 2 \text{ parts} \times 16 \text{ pence per part} = 32 \text{ pence} \][/tex]
### Conclusion
Therefore, dividing 80 pence into two parts in the ratio [tex]\( 3:2 \)[/tex] gives:
- First portion: 48 pence
- Second portion: 32 pence
