Problem 279

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 $30\times2=60$ 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 $40\div2=20$ chickens.

(We may check that if there are 20 chickens, then there are $30-20=10$ emus, and Karl would then give out $4\times20+2\times10=100$ 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 $5\times2+25\times4=110$ 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.

Therefore, Karl has 20 chickens.