At a certain college last year, a total of 260 students took College Algebra in either the fall semester or the spring semester or both. If 40 students took College Algebra in both semesters and twice as many students took College Algebra in the fall semester as in the spring semester, how many students took College Algebra in the fall semester last year?Key to getting this question correct is to notice the following. If "260 students took College Algebra in either the fall semester or the spring semester or both," then all 260 took College Algebra in one or both semesters, and none of the 260 took College Algebra in neither semester.
Using that information, we can set up the following equation, with
x representing the number of students who took College Algebra in the spring semester.
260 = Number Who Took in Fall + Number Who Took in Spring - Number Who Took in Both + Number Who Took in Neither
260 = 2
x +
x - 40 + 0
300 = 3
x100 =
x = Number Who Took in Spring
Question asked:
how many students took College Algebra in the fall semester last year? Number Who Took in Fall = 2 × Number Who Took in Spring = 2 × 100 = 200
A. 73
B. 100
C. 142
D. 160
E. 200Correct answer: E