Let's solve this problem step-by-step:
### Part (a): Calculating the Number of Tins Needed
Given:
- One tin of creosote paint covers 9 square meters of fencing.
- The total area of the fence that needs to be covered is 102.5 square meters.
To find out the number of tins needed, we need to divide the total area by the area that one tin can cover.
[tex]\[ \text{Number of tins needed} = \frac{\text{Total area to cover}}{\text{Area covered by one tin}} \][/tex]
Substituting the given values:
[tex]\[ \text{Number of tins needed} = \frac{102.5 \text{ square meters}}{9 \text{ square meters per tin}} \][/tex]
Perform the division:
[tex]\[ \text{Number of tins needed} = 11.388 \][/tex]
Since we cannot purchase a fraction of a tin, we will round up to the next whole number:
[tex]\[ \text{Number of tins needed} = 12 \][/tex]
So, you will need 12 tins to cover the entire area of the fence.
### Part (b): Calculating the Total Cost
Given:
- The cost of one tin is [tex]\( £6.50 \)[/tex].
- You need 12 tins.
To find out the total cost, we multiply the number of tins by the cost per tin.
[tex]\[ \text{Total cost} = \text{Number of tins needed} \times \text{Cost per tin} \][/tex]
Substituting the given values:
[tex]\[ \text{Total cost} = 12 \times £6.50 \][/tex]
Perform the multiplication:
[tex]\[ \text{Total cost} = £78.00 \][/tex]
So, you will have to pay £78.00 for the 12 tins of creosote paint.
### Final Answer:
(a) You will need 12 tins to cover a fence with an area of 102.5 square meters.
(b) The total cost will be £78.00.
