Question

Davis electronics manufactures a certain type of radio that requires 15 working resistors per radio. If one out of 25 resistors is defective, are 30,150 resistors enough to assemble 1922 radios?

Answer 1

To determine if 30,150 resistors is enough to make 1,922 radios, we do ratio and proportion. In this kind of solution, we base it on a fixed ratio as given by 15 working resistors is to 1 radio. Moreover, you are given an additional detail of probability. All you have to do is multiply the probability to the total resistors to determine the exact amount of working resistors. Since the probability of defect is 1/25, by difference, the probability of a working resistor is 1-1/25 = 24/25.

Therefore,

15/1 ≤ 30150(24/25)/1922
15 ≤ 15.06

The symbol '≤' means less than or equal to. It is the inequality to be used because 15/1 is the minimum limit. As long as the ratio is equal to 15 or more than 15, then 30,150 is enough to make 1,922 radio. Since it is true that 15.06 is greater than 15, then the amount of resistors would be enough.