CHECK YOUR BRAIN
<pre class="tw-data-text vk_txt tw-ta tw-text-small" data-placeholder="Translation" id="tw-target-text" data-fulltext="" dir="ltr" style="unicode-bidi: isolate; font-family: inherit; border: none; padding: 0px 0.14em 0px 0px; position: relative; margin-bottom: 0px; resize: none; overflow: hidden; width: 237.5px; white-space: pre-wrap; color: rgb(33, 33, 33); height: 96px; font-size: 16px !important; line-height: 24px !important; background-color: rgb(255, 255, 255);">There are a few ducks and goats in a field . Overall, 77 heads and 224 feet . What is the number of ducks ?</pre>

It depends on how many 3-legged goats and one-legged ducks there are.&nbsp;

duck = xgoat = yx + y = 77-------&gt; x = 77 - y2x + 4y = 224 -----&gt; simplified --------&gt; x + 2y = 112(77 - y) + 2y = 11277 - y + 2y = 112y = 112 - 77&nbsp;y = 35 so, x = 77 - yx = 77 - 35 = 4242 ducks

Let's all goats and &nbsp;ducks raise two feet. So 224-77*2 feet left, that's 70 feet. All goats fall down. Each ducks left 2 feet on ground. So there are half of 70 ducks, that's 35.