Question

At a certain college, ten percent of freshmen enter without a major declared. Of those who enter with a major declared, twenty percent change it by the end of their second year. If the college admits 150 freshmen this year, how many will end their second year with the major they declared upon entry?

Answer 1

Step-by-step explanation:

10% enter without a declared major.

ok.

that means

100% - 10% = 90%

enter with a declared major.

of those 90%, 20% (that means now 20% of the 90%) change their major by the end of the second year.

that means

100% - 20% = 80% (of these 90%)

keep their declared major until the end of the seconds year.

now,

20% of 90% = 90/100 × 20 = 0.9 × 20 = 18% of the original 100%

and therefore,

80% of 90% = 90/100 × 80 = 0.9 × 80 = 72% of the original 100%.

100% = 150

1% = 100%/100 = 150/100 = 1.5

72% = 72 × 1% = 72 × 1.5 = 108

108 of these starting 150 freshmen will end their second year with the major they declared upon entry.