An electronics company finds that 5 out of 75 capacitors produced are damaged. How many damaged items can they expect if the company produces 1,500 capacitors?

Explanation:

5/75 = 1/15 means that 1 out of every 15 capacitors are damaged.

Multiplying this with the 1500 capacitors produced, we expect about (1/15)*1500 = 1500/15 = 100 capacitors are damaged in this batch.

A slightly different approach:

Saying "1 out of every 15 capacitors are damaged" means we can form the ratio

1 damaged: 15 total

Then multiply both sides by 100 so that the "15 total" jumps up to "1500 total" and we get the following

1 damaged: 15 total

100*(1 damaged): 100*(15 total)

100 damaged: 1500 total

We get the same answer as before.

Keep in mind that it's not a guarantee that we'll find 100 damaged capacitors out of 1500 total, but rather this is an estimate based on the average. So instead of saying "there are 100 damaged capacitors" it would be better to say "there are expected to be about 100 damaged capacitors".

the mean and mad

step-by-step explanation: