To solve the problem of sharing £14.40 in the ratio 2:3:7, follow these steps:
### Step 1: Understanding the Ratio
The ratio given is 2:3:7. This means the total amount (£14.40) should be divided into parts such that:
- The first part is 2 parts,
- The second part is 3 parts,
- The third part is 7 parts.
### Step 2: Calculating the Sum of the Parts
First, we need to calculate the total number of parts in this ratio.
[tex]\[
2 + 3 + 7 = 12
\][/tex]
This tells us that the total amount will be divided into 12 equal parts.
### Step 3: Determining the Value of One Part
Next, we need to find out how much each part is worth by dividing the total amount by the sum of the parts.
[tex]\[
\frac{£14.40}{12} = £1.20
\][/tex]
This means that each part of the ratio is worth £1.20.
### Step 4: Calculating Each Share
Now, let's determine the monetary value of each share using the ratio parts.
- For the first share (2 parts):
[tex]\[
2 \times £1.20 = £2.40
\][/tex]
- For the second share (3 parts):
[tex]\[
3 \times £1.20 = £3.60
\][/tex]
- For the third share (7 parts):
[tex]\[
7 \times £1.20 = £8.40
\][/tex]
### Step 5: Verifying the Total
To ensure our calculations are correct, we can add up the three amounts to see if they sum to £14.40:
[tex]\[
£2.40 + £3.60 + £8.40 = £14.40
\][/tex]
### Conclusion
Thus, the £14.40 is shared in the ratio 2:3:7 as follows:
- The first share is £2.40,
- The second share is £3.60,
- The third share is £8.40.
