one fifth of all value lamps are already defect at the time of purchase. how many has frank got to buy in order to ensure that he has 16 functioning lamps?

Question

one fifth of all value lamps are already defect at the time of purchase. how many has frank got to buy in order to ensure that he has 16 functioning lamps?

Answer 1

Let x = number of value lamps bought

 

(1/5)x = number of defective lamps

(4/5)x = number of good lamps

 

(4/5)x = 16

 

solve for x

4x = (16)*5

x = 80/4

x = 20 lamps

Answer 2

Hi Shannon,

 

Let's begin by assigning a letter for our unknown:

    x (number of lamps bought)

 

Now let's represent in terms of x that 1/5 (20%) of bought lamps are defective.  This is equivalent to saying that 4/5 (80%) of bought lamps are good.  We'll use this equivalent statement since we are told how many lamps are good:

    0.8x (number of good lamps)

 

Now we'll set up an equation using our expression for the number of good lamps:

    0.8x = 16

 

Finally, we'll solve this equation for our unknown (x):

    0.8x = 16

        x = 16/0.8

        x = 20 (numner of bought lamps)

 

The trick to solving this problem was coming up with the right expression for the number of good lamps in terms of our unknown (number of bought lamps).

 

Thanks for submitting this problem.

 

God bless, Jordan.