Question

the combined average weight of an okapi and a llama is 450 kilograms. the average weight of 3 llamas is 190 kilograms more than the average weight of one okapi. on average, how much does an okapi weigh, and how much does a llama weigh? on average, an okapi weighs \boxed{} kilograms and a llama weighs \boxed{} kilograms.

Explanation:

Step1: Define variables

Let \( o \) be the weight of an okapi (in kg) and \( l \) be the weight of a llama (in kg).
From the first condition: \( o + l = 450 \) (Equation 1)
From the second condition: \( 3l = o + 190 \) (Equation 2)

Step2: Solve the system of equations

From Equation 1, we can express \( o = 450 - l \).
Substitute \( o = 450 - l \) into Equation 2:
\( 3l = (450 - l) + 190 \)
Simplify the right - hand side: \( 3l = 450 + 190 - l \)
\( 3l + l = 640 \)
\( 4l = 640 \)
Divide both sides by 4: \( l=\frac{640}{4}=160 \)

Step3: Find the weight of the okapi

Substitute \( l = 160 \) into Equation 1: \( o+160 = 450 \)
Subtract 160 from both sides: \( o = 450 - 160 = 290 \)

Answer:

On average, an okapi weighs \( \boldsymbol{290} \) kilograms and a llama weighs \( \boldsymbol{160} \) kilograms.