Math / Algebra

QuestionThe 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 $\qquad$ kilograms and a llama weighs $\qquad$ kilograms.

Studdy Solution

STEP 1

What is this asking? We need to find the average weight of an okapi and a llama, given their combined average and the relationship between the average weights of multiple llamas and a single okapi. Watch out! Don't mix up the combined average with the average of each animal.
Also, be careful with the difference in number of llamas when comparing their average weight to the okapi's.

STEP 2

1. Set up variables and equations.
2. Solve for the average weight of an okapi.
3. Solve for the average weight of a llama.

STEP 3

Let's define some variables to make things easier!
Let $o$ be the average weight of an okapi, and $l$ be the average weight of a llama.

STEP 4

The problem says the combined average weight of an okapi and a llama is 450 kilograms.
This means $\frac{o + l}{2} = 450$ .
We're dividing by two because we're averaging the weight of two animals.
This is our first equation.

STEP 5

The problem also says the average weight of 3 llamas is 190 kilograms more than the average weight of one okapi.
The average weight of 3 llamas is $\frac{3l}{3}$ , which simplifies to just $l$ .
So, our second equation is $l = o + 190$ .

STEP 6

We can substitute the expression for $l$ from our second equation ( $l = o + 190$ ) into our first equation: $\frac{o + (o + 190)}{2} = 450$ .
We're doing this to get an equation with only one variable, $o$ , which we can solve!

STEP 7

Now, let's simplify and solve for $o$ .
First, combine the $o$ terms in the numerator: $\frac{2o + 190}{2} = 450$ .
Then, multiply both sides of the equation by 2 to get rid of the fraction: $2o + 190 = 900$ .
Next, subtract 190 from both sides: $2o = 710$ .
Finally, divide both sides by 2: $o = 355$ .
So, the average weight of an okapi is 355 kilograms!

STEP 8

Now that we know $o = 355$ , we can plug this value back into our second equation ( $l = o + 190$ ) to find $l$ : $l = 355 + 190$ .

STEP 9

Adding those numbers together, we get $l = 545$ .
So, the average weight of a llama is 545 kilograms!

STEP 10

On average, an okapi weighs $355$ kilograms and a llama weighs $545$ kilograms.

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Studdy Solution

STEP 1

STEP 2

1. Set up variables and equations.
2. Solve for the average weight of an okapi.
3. Solve for the average weight of a llama.

STEP 3

Let's define some variables to make things easier!
Let $o$ be the average weight of an okapi, and $l$ be the average weight of a llama.

STEP 4

The problem says the combined average weight of an okapi and a llama is 450 kilograms.
This means $\frac{o + l}{2} = 450$ .
We're dividing by two because we're averaging the weight of two animals.
This is our first equation.

STEP 5

The problem also says the average weight of 3 llamas is 190 kilograms more than the average weight of one okapi.
The average weight of 3 llamas is $\frac{3l}{3}$ , which simplifies to just $l$ .
So, our second equation is $l = o + 190$ .

STEP 6

We can substitute the expression for $l$ from our second equation ( $l = o + 190$ ) into our first equation: $\frac{o + (o + 190)}{2} = 450$ .
We're doing this to get an equation with only one variable, $o$ , which we can solve!

STEP 7

STEP 8

Now that we know $o = 355$ , we can plug this value back into our second equation ( $l = o + 190$ ) to find $l$ : $l = 355 + 190$ .

STEP 9

Adding those numbers together, we get $l = 545$ .
So, the average weight of a llama is 545 kilograms!

STEP 10

On average, an okapi weighs $355$ kilograms and a llama weighs $545$ kilograms.

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Studdy Solution

STEP 1

STEP 2

1. Set up variables and equations.2. Solve for the average weight of an okapi.3. Solve for the average weight of a llama.

STEP 3

Let's **define** some variables to make things easier!Let ooo be the average weight of an okapi, and lll be the average weight of a llama.

STEP 4

The problem says the combined average weight of an okapi and a llama is 450 kilograms.This means o+l2=450\frac{o + l}{2} = 4502o+l​=450.We're dividing by **two** because we're averaging the weight of *two* animals.This is our **first equation**.

STEP 5

The problem also says the average weight of 3 llamas is 190 kilograms *more* than the average weight of one okapi.The average weight of 3 llamas is 3l3\frac{3l}{3}33l​, which simplifies to just lll.So, our **second equation** is l=o+190l = o + 190l=o+190.

STEP 6

We can **substitute** the expression for lll from our second equation (l=o+190l = o + 190l=o+190) into our first equation: o+(o+190)2=450\frac{o + (o + 190)}{2} = 4502o+(o+190)​=450.We're doing this to get an equation with only *one* variable, ooo, which we can solve!

STEP 7

STEP 8

Now that we know o=355o = 355o=355, we can **plug** this value back into our second equation (l=o+190l = o + 190l=o+190) to find lll: l=355+190l = 355 + 190l=355+190.

STEP 9

Adding those numbers together, we get l=545l = 545l=545.So, the average weight of a llama is **545 kilograms**!

STEP 10

On average, an okapi weighs 355355355 kilograms and a llama weighs 545545545 kilograms.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Set up variables and equations.
2. Solve for the average weight of an okapi.
3. Solve for the average weight of a llama.

Let's define some variables to make things easier!
Let $o$ be the average weight of an okapi, and $l$ be the average weight of a llama.

The problem says the combined average weight of an okapi and a llama is 450 kilograms.
This means $\frac{o + l}{2} = 450$ .
We're dividing by two because we're averaging the weight of two animals.
This is our first equation.

The problem also says the average weight of 3 llamas is 190 kilograms more than the average weight of one okapi.
The average weight of 3 llamas is $\frac{3l}{3}$ , which simplifies to just $l$ .
So, our second equation is $l = o + 190$ .

We can substitute the expression for $l$ from our second equation ( $l = o + 190$ ) into our first equation: $\frac{o + (o + 190)}{2} = 450$ .
We're doing this to get an equation with only one variable, $o$ , which we can solve!

Now that we know $o = 355$ , we can plug this value back into our second equation ( $l = o + 190$ ) to find $l$ : $l = 355 + 190$ .

Adding those numbers together, we get $l = 545$ .
So, the average weight of a llama is 545 kilograms!

On average, an okapi weighs $355$ kilograms and a llama weighs $545$ kilograms.