# A killer whale has eaten 75 pounds of fish today. It needs to eat at least 140 pounds of fish each day A bucket holds 15 pounds of fish. Identify an inequality that represents how many more buckets z of fish the whale needs to eat?

Dec 13, 2016

$\text{If the count of buckets is "x" then we have: } x \ge 4 \frac{1}{3}$

#### Explanation:

Let the count of buckets needed be $x$

$\textcolor{b l u e}{\text{Determine the amount left that needs to be consumed}}$

For now drop the unit of measurement of lb

Total needed - total eaten so far = remainder to eat

$\textcolor{g r e e n}{140 - 75 = 65}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the exact count of bucket loads}}$

quantity in 1 bucket x count of buckets = remainder to eat

$15 x = 65$

divide both sides by 15

$\frac{15}{15} x = \frac{65}{15}$

But $\frac{15}{15} = 1$

$x = \frac{65}{15} = 4.3333 \ldots$ as an exact value

but 0.33333...$= \frac{1}{3}$

$x = 4 \frac{1}{3}$ buckets
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Write this as an inequality}}$

At least $4 \frac{1}{3}$ buckets is the same as:

Greater than or equal to which is written as $\ge$ or $\le$ depending on which way things are.

Thus we have:

The count of buckets is greater than or equal to $4 \frac{1}{3}$

$\implies x \ge 4 \frac{1}{3}$