Question

The elves and reindeer are getting ready for a meeting with Santa.

So far 14 of them have arrived.
If they have 38 legs between them, how many reindeer are at the meeting and how many elves are at the meeting?
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Answer 1

To solve the problem, create a system of equations using the given information and solve for the values of x and y.

Step-by-step explanation:

To solve this problem, let's assign variables to represent the number of elves and reindeer. Let's say the number of elves is x and the number of reindeer is y.

From the problem, we know that the total number of elves and reindeer is 14, so we can write the equation:

x + y = 14

We also know that the total number of legs is 38. Since each elf has 2 legs and each reindeer has 4 legs, we can write another equation:

2x + 4y = 38

We can solve this system of equations to find the values of x and y. Multiplying the first equation by 2, we get:

2x + 2y = 28

Subtracting this equation from the second equation, we obtain:

2x + 4y - (2x + 2y) = 38 - 28

Simplifying, we get:

2y = 10

Dividing both sides by 2, we find that y = 5. Substituting this value back into the first equation, we can solve for x:

x + 5 = 14

x = 14 - 5

x = 9

Therefore, there are 9 elves at the meeting and 5 reindeer.

Answer 2

Let
`e` and
`r` be the number of elves and reindeers, respectively.

We know that:

`r+e=14` (so far 14 of them have arrived)

`4r+2e = 38`(each reindeer has 4 legs and each elf has two)

If we multiply the first equation by 2 we have
`2r+2e=28`, and if we subtract this equation from the second we have
`2r=10` which implies
`r=5`.

So, there are 5 reindeers and 9 elves (remember that they have to sum up to 14).