Question

The minimum weight of every cake that Ben’s bakery bakes is $100$ pounds. A customer wants a cake that doesn’t weigh more than $150$ pounds. Which of the following inequalities represents the range between which the weight of the cake $\left(x\right)$ (in pounds) ordered by the customer would lie in?

• A. $80<x<120$
• B. $90\le x<100$
• C. $110<x\le 140$
• D. $110\le x\le 160$

Answer 1

The correct option is C $110<x\le 140$

Let the weight of the cake ordered by the customer be $xlb.$
Now, the minimum weight of every cake sold by the bakery is $100lb.$

$\Rightarrow 100\le x.........\left(1\right)$
The customer doesn’t want their cake to weigh more than $150lb.$ This means that the cake can either weigh exactly $150lb$ or less than $150lb.$


$\Rightarrow x\le \mathrm{150........}\left(2\right)$
Combining (1) and (2) we get: $100\le x\le 150$

Among the given options, only option B fits in the interval $100\le x\le 150.$
Option B: $110<x\le 140$

The lower limit is $110$ and it lies in between $100$ and $150.$ The upper limit is $140$ and it lies in between $100$ and $150.$ If
$x$ takes any value between $110$ and $140,$ it will automatically be in between $100$ and $150.$
Therefore, option B is correct.