To solve this problem, we need to determine the cost per centimeter of ribbon at each shop and then use this information to find the total cost for 300 centimeters of ribbon at each shop. Finally, we will find the difference in the prices.
### Step-by-Step Solution
1. Calculate the cost per centimeter of ribbon for each shop:
- Shop A:
[tex]\[
\text{Length of ribbon} = 120 \, \text{cm}, \quad \text{Cost} = £1.56
\][/tex]
The cost per centimeter (cm) is given by dividing the total cost by the total length of the ribbon:
[tex]\[
\text{Cost per cm} = \frac{1.56}{120} = £0.013 \, \text{per cm}
\][/tex]
- Shop B:
[tex]\[
\text{Length of ribbon} = 185 \, \text{cm}, \quad \text{Cost} = £1.48
\][/tex]
The cost per centimeter (cm) is given by:
[tex]\[
\text{Cost per cm} = \frac{1.48}{185} = £0.008 \, \text{per cm}
\][/tex]
2. Calculate the total cost for 300 centimeters of ribbon at each shop:
- For Shop A:
[tex]\[
\text{Total cost for 300 cm} = 300 \, \text{cm} \times £0.013 \, \text{per cm} = £3.90
\][/tex]
- For Shop B:
[tex]\[
\text{Total cost for 300 cm} = 300 \, \text{cm} \times £0.008 \, \text{per cm} = £2.40
\][/tex]
3. Calculate the difference in cost between the two shops:
- The difference in the total cost for 300 cm of ribbon is:
[tex]\[
\text{Cost difference} = £3.90 - £2.40 = £1.50
\][/tex]
### Final Answer
The difference in the price of 300 cm of ribbon between Shop A and Shop B is £1.50.
