To determine the total cost of the oil bottles that Gary needs to buy, let's go through the problem step-by-step:
1. Total Distance and Consumption Rate:
- Gary plans to ride 3000 miles.
- His motorbike consumes 1 liter of the oil and petrol mixture for every 20 miles.
2. Total Liters of Mixture Needed:
- First, we calculate how many liters of the mixture are required for the entire trip.
- Since the bike consumes 1 liter for every 20 miles, the total liters needed are:
[tex]\[
\text{Total liters needed} = \frac{\text{Total distance}}{\text{Consumption rate per mile}} = \frac{3000 \text{ miles}}{20 \text{ miles per liter}} = 150 \text{ liters}
\][/tex]
3. Oil to Petrol Ratio:
- The oil to petrol ratio by volume is 1:14.
- This means for every 1 part of oil, there are 14 parts of petrol.
- The total ratio of oil to petrol is [tex]\(1 + 14 = 15\)[/tex].
4. Liters of Oil Needed:
- To find out how much oil is needed, we use the ratio to break down the total mixture.
- The proportion of oil in the mixture can be calculated as:
[tex]\[
\text{Oil needed (liters)} = \left( \frac{\text{Oil part}}{\text{Total ratio}} \right) \times \text{Total liters needed} = \left( \frac{1}{15} \right) \times 150 = 10 \text{ liters}
\][/tex]
5. Convert Liters to Milliliters:
- We know that 1 liter = 1000 milliliters (ml).
- Therefore, 10 liters of oil is equivalent to:
[tex]\[
\text{Oil needed (ml)} = 10 \text{ liters} \times 1000 \text{ ml/liter} = 10000 \text{ ml}
\][/tex]
6. Number of Bottles Needed:
- Gary needs to buy oil that comes in 1000 ml bottles.
- The number of bottles required is:
[tex]\[
\text{Bottles needed} = \frac{\text{Oil needed (ml)}}{\text{Bottle size (ml)}} = \frac{10000 \text{ ml}}{1000 \text{ ml/bottle}} = 10 \text{ bottles}
\][/tex]
7. Total Cost of Oil Bottles:
- Each bottle of oil costs £9.
- Therefore, the total cost for 10 bottles is:
[tex]\[
\text{Total cost} = \text{Number of bottles} \times \text{Cost per bottle} = 10 \times £9 = £90
\][/tex]
So, the total cost of the bottles of oil that Gary needs to buy is £90.
