Coal truck
What percentage of the truck's final mass is coal?
Problem
The mass of an empty coal truck before it is loaded is 2000 kg.
At the start of a day it is loaded with coal, and the coal makes up 80% of the total mass.
At the first delivery, the driver unloads a quarter of the coal.
Can you express the mass of coal left on the truck, as a percentage of the total mass, after the driver made the first delivery?
This problem is adapted from the World Mathematics Championships
Student Solutions
Answer: 75%
Using ratio
At the beginning of the day, the mass of the truck is 80% coal and 20% truck.
Ratio of truck : coal is 1 : 4
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At the first delivery, the truck loses $\frac14$ of the coal:
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So the ratio of truck : coal is 1 : 3. That is equivalent to 25% : 75%.
So 75% of the truck's mass is coal after the first delivery.
Finding the total mass of the truck and the load
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$6000$ kg coal
total mass $8000$ kg.
$\dfrac{6000}{8000}=\dfrac34=75\%$ of the total mass is coal.