How would one work this out? (Fractions)

Question

One fifth of all value lamps are already defected at the time of purchase. How many do you have to buy to ensure that you have 16 functioning lamps.?

Anyone have any advice on how to layout this question mathematically? I struggle to put these sorts of questions in to a calculation.

Answer 1

Hint:

If $x$ is the number of lamp to buy, you want: $$ x-\dfrac{x}{5}=16 $$

can you solve?

Answer 2

Consider this:

Among all the lamps you've purchased (the whole box), there are always $\frac 15$ of them broken

(smaller box). In other words, there are $\frac 45$ of them ($16$ lamps) NOT broken (the larger box).

So how can you evaluate the required amount of lamps to be brought (the whole box)?

Answer 3

Let,number of lamps to be purchased=$$x$$.Now,number defective=$$\frac {x}{5}$$.So,working lamps=$x$-$\frac {x}{5}$.Now you want 16 working lamps.So, $x$-$\frac {x}{5}$=16.Solving,you get $x=20$.