Question

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance? (A) 45% (B) 56% (C) 64% (D) 75% (E) 80%

Answer 1

The correct option is C

Explanation:

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year

Let x = the attendance for last year

The projected attendance for this year would be last year's attendance + 25% of last year's attendance. This means

Projected attendance for this year

= x + 25/100 × x

= x + 0.25x = 1.25x

But attendance for this year actually decreased by 20 percent.

This means the actual attendance for this year would be

attendance for last year - 20% of attendance for last year. This means

Actual attendance for this year is

x - 20/100 × x

= x - 0.2x = 0.8x

percentage of the projected attendance that was the actual attendance would be

0.8x / 1.25x × 100 = 0.64 × 100

= 64%

The correct option is C