Question

Extra clothes weigh 4/3 lb and food weighs 1/4 lb. If Joe wants to leave more than 5 lb of luggage, the minimum weight of tea that he must leave is

• A. 19/4 lb
• B. 41/12 lb
• C. 19/12 lb
• D. 41/4 lb

Answer 1

The correct option is B 41/12 lb

Let the tea left be $y$ lb.
Weight of extra clothes = $\frac{4}{3}$ lb
Weight of food = $\frac{1}{4}$ lb

So, in order to leave atleast 5 lb of his luggage, the weight of the tea package needs to be added such that the total weight of the tea package, food, and clothes is greater than 5.
i.e.,

$y$ + $\frac{4}{3}$ + $\frac{1}{4}$ > 5

$\Rightarrow$ $y$ + $\frac{16+3}{12}$ > 5

$\Rightarrow$ $y$ +$\frac{19}{12}$ > 5

$\Rightarrow$ $y$ + $\frac{19}{12}$ - $\frac{19}{12}$ > 5 - $\frac{19}{12}$

$\Rightarrow$ $y$ > 5 - $\frac{19}{12}$

$\Rightarrow$ $y$ > $\frac{41}{12}$ lb