Question

In 1990, 75% of all high school seniors had jobs. In 2010, 40% of all seniors had jobs. If there were 50 more seniors in 2010 than 1990 and there were a total of 403 jobs between both years, how many seniors were there in 1990? How many seniors had jobs in 2010

Answer 1

There were 333 seniors in 1990

153 seniors had jobs in 2010.

Explanation:

Let the number of high school seniors in 1990 = x

75% of x had jobs in 1990

In 2010 there were 50 more seniors. That is, the number of seniors is x+50.

40% of (x+50) had jobs in 2010.

Total number of jobs in both years = 403.

\[0.75 * x + 0.4 * (x + 50) = 403\]

\[0.75 * x + 0.4 * x + 20 = 403\]

=> \[1.15 * x = 403 - 20\]

=> \[1.15 * x = 383\]

=> \[x = 383/1.15\]

=> \[x = 333\]

Number of seniors having job in 2010 = 0.4 * (333 + 50) = 0.4 * 383 = 153.2 = 153(approx)