Karl has 30 birds. Some of his birds are emus and the rest are chickens. Karl hands out 100 treats to his birds. Each emu gets 2 treats and each chicken gets 4 treats. How many chickens does Karl have?
(A) 10
(B) 15
(C) 25
(D) 20
(E) 6
Solution 1

Since each emu gets 2 treats and each chicken gets 4 treats, each of Karl's 30 birds gets at least 2 treats .

If Karl begins by giving his 30 birds exactly 2 treats each, then Karl will have given out $30 \times 2=60$ of the treats.

Since Karl has 100 treats to hand out, then he has $100-60=40$ treats left to give.

However, each emu has already received their 2 treats (since all 30 birds were given 2 treats).

So the remaining 40 treats must be given to chickens.

Each chicken is to receive 4 treats and has already received 2 treats.

Therefore, each chicken must receive 2 more treats.

Since there are 40 treats remaining, and each chicken receives 2 of these treats, then there are $40 \div 2=20$ chickens.

(We may check that if there are 20 chickens, then there are $30-20=10$ emus, and Karl would then give out $4 \times 20+2 \times 10=100$ treats.)

## Solution 2

Using a trial and error approach, if Karl had 5 emus and $30-5=25$ chickens, then he would need to hand out $5 \times 2+25 \times 4=110$ treats.

Since Karl hands out 100 treats, we know that Karl has more emus than 5 (and fewer chickens than 25).

We show this attempt and continue with this approach in the table below.

| Number  of Emus | Number  of Chickens | Number of  Emu Treats | Number of  Chicken Treats | Total Number  of Treats |
| :---: | :---: | :---: | :---: | :---: |
| 5 | $30-5=25$ | $5 \times 2=10$ | $25 \times 4=100$ | $10+100=110$ |
| 7 | $30-7=23$ | $7 \times 2=14$ | $23 \times 4=92$ | $14+92=106$ |
| 10 | $30-10=20$ | $10 \times 2=20$ | $20 \times 4=80$ | $20+80=100$ |

Therefore, Karl has 20 chickens.

ANSWER: (D)

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