Math word problem

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?

Answer 1

First, we consider what we know and express that data algebraically.

Let's use the variable 'o' for okapi and variable 'l' for llama.

O + L = 450 (kilograms)

And the average weight of three llamas is the weight of an okapi plus 190 kilograms.

So this can be expressed with:

3L = O + 190 (kilograms)

One way to solve this is to distribute a three to the (O+L) term and the 450 term because we want to solve for okapi.

So the result is:

3O + 3L = 1350

Since we know what 3L is in terms of kilograms and okapi, given to us by the second statement, let's substitute that 3L for O+190.

3O + O + 190 = 1350

Now, let's move like terms to their respective sides of the equation and combine them.

4O = 1160

Then let's divide by the coefficient of okapi, which is four.

The average weight of an okapi is 290 kg.

If we insert that known value into our first equation and solve for the average weight of a llama, or...

290 + L = 450

L = 160 kg

Finally check by inserting the values of the average weights back into either (or both) equations:

The average weight of an okapi plus the average weight of a llama equals 450 kilograms.

290 + 160 = 450; true

The average weight of three llamas is 190 kilograms more than the average weight of an okapi.

3(160) = 290 + 190

480 = 290 + 190; true

Hope this helps!

Answer 2

If we let O represent the average weight of an Okapi and L represent the llama, then

O + L = 450 and

3L = 190 + O

Let's solve the bottom equation for O.

O = 3L - 190

Substitute that into the top equation

3L - 190 + L = 450

Combine like terms and solve for L

Then plug that back in to find O.