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?

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. $\frac{1}{2}M$ 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 $\frac{1}{2}M$. So, they ate $\frac{1}{2} \times \frac{1}{2}M = \frac{1}{4}M$. Subtracting this from the meat left after the T-Rex gives us $\frac{1}{2}M - \frac{1}{4}M = \frac{1}{4}M$ of meat remaining.

Step 4: Allosaurus gulps the rest

The remaining meat, which is $\frac{1}{4}M$, 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 $\frac{1}{4}M = 270$ kg by 4. This gives us the initial total mass of the triceratops meat.

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