Question

On a farm in iowa lived grandpa bill in a big yellow house on the top of the hill. His 70th birthday was this very day. All of his family were on their way. His wife sue had baked a cake. They'd all eat it by the lake. After the party the grandkids would play with all of the dogs then roll in the hay. He'd look out the window and what would he see? EIGHTY-FOUR legs and heads THIRTY-THREE!! grandpa Bill's question for you is not very hard. How many dogs and grandchildren will be in the yard? ​

Answer 1

Let g be the number of grandchildren, and d be the number of dogs. They both have only one head, so the number of heads is

$g+d=33$

Grandchildren have 2 legs, while dogs have 4. So, the total number of legs is

$2g+4d=84$

From the first equation (the one for the heads) we can derive

$g=33-d$

Substitute this into the second to get

$2g+4d=84 \implies 2(33-d)+4d=84 \iff 2d=18 \iff d=9$

So, there are 9 dogs and (from the first equation

$g=33-9=24$