There are 110,000 litres of petrol in total available in a chain of four petrol stations. Station A has three times as much as Station C. Station B has 24,200 litres more than Stat... There are 110,000 litres of petrol in total available in a chain of four petrol stations. Station A has three times as much as Station C. Station B has 24,200 litres more than Station A. Station D has 24,200 litres more than Station C. Adjust the pie chart to represent the amount of petrol at each station (rounding to the nearest whole number only in the last step).
Understand the Problem
We have four petrol stations (A, B, C, and D) with a total of 110,000 litres of petrol in total. Station A has three times as much petrol as Station C. Station B has 24,200 litres more than Station A. Station D has 24,200 litres more than Station C. Our goal is to determine the amount of petrol at each station and adjust the pie chart accordingly.
Answer
Station A: 21% Station B: 43% Station C: 7% Station D: 29%
Answer for screen readers
Station A: 21% Station B: 43% Station C: 7% Station D: 29%
Steps to Solve
- Define variables
Let's assign variables to represent the amount of petrol at each station: $A$ = amount of petrol at Station A $B$ = amount of petrol at Station B $C$ = amount of petrol at Station C $D$ = amount of petrol at Station D
- Write equations based on the given information
We can express the given information as equations:
Station A has three times as much petrol as Station C: $A = 3C$
Station B has 24,200 litres more than Station A: $B = A + 24200$
Station D has 24,200 litres more than Station C: $D = C + 24200$
The total amount of petrol is 110,000 litres: $A + B + C + D = 110000$
- Substitute to create a single equation
Substitute $A$, $B$, and $D$ in terms of $C$ into the total amount equation:
$3C + (3C + 24200) + C + (C + 24200) = 110000$
- Simplify and solve for $C$
Combine like terms:
$8C + 48400 = 110000$
Subtract 48400 from both sides:
$8C = 61600$
Divide by 8: $C = 7700$
- Solve for A, B, and D
Now that we have the value of $C$, we can find $A$, $B$, and $D$:
$A = 3C = 3(7700) = 23100$
$B = A + 24200 = 23100 + 24200 = 47300$
$D = C + 24200 = 7700 + 24200 = 31900$
- Calculate the percentage of petrol at each station
To adjust the pie chart, we need to find the percentage of the total petrol at each station:
Percentage at Station A: $\frac{23100}{110000} \times 100 = 21%$
Percentage at Station B: $\frac{47300}{110000} \times 100 = 43%$
Percentage at Station C: $\frac{7700}{110000} \times 100 = 7%$
Percentage at Station D: $\frac{31900}{110000} \times 100 = 29%$
Station A: 21% Station B: 43% Station C: 7% Station D: 29%
More Information
The percentages of petrol at each station add up to 100%, confirming the correctness of the solution.
Tips
A common mistake is an arithmetic error when simplifying and solving the equations. Double-checking your work is always helpful. Another error might be misinterpreting the relationships between the stations, especially with the "more than" statements.
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