A Tyrannosaurus rex ate half of a small triceratops it had hunted. When it left, a pack of velociraptors scavenged half of what was left. A group of lazy Allosaurus gulped down the last 270 kilograms of meat. How many kilograms of meat were on the triceratops before the T-Rex ate?
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Step-by-Step Solution
Step 1: Define variables
Let M represent the total mass of the triceratops meat in kilograms before any animal ate it. This is the quantity we need to find.
Step 2: T-Rex eats half
The Tyrannosaurus rex ate half of the triceratops. To find the remaining meat, we subtract half of the total meat from the total meat. 21M of meat was left after the T-Rex ate.
Step 3: Velociraptors scavenge half of what was left
The velociraptors scavenged half of what was left, which was 21M. So, they ate 21×21M=41M. Subtracting this from the meat left after the T-Rex gives us 21M−41M=41M of meat remaining.
Step 4: Allosaurus gulps the rest
The remaining meat, which is 41M, was eaten by the Allosaurus. We are given that this amount is 270 kilograms. We set up an equation to represent this relation.
Step 5: Solve for M
To find the total meat M, we multiply both sides of the equation 41M=270 kg by 4. This gives us the initial total mass of the triceratops meat.