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The owners of a traveling televangelist circuit projected a 30 percent

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
The owners of a traveling televangelist circuit projected a 30 percent  [#permalink]

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01 Jan 2018, 10:37
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Difficulty:

25% (medium)

Question Stats:

95% (01:34) correct 5% (01:24) wrong based on 22 sessions

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The owners of a traveling televangelist circuit projected a 30 percent increase in attendance this year over last year. The actual attendance this year was 15 percent less than last year's attendance. Approximately, what percent of the projected attendance was the actual attendance?

A. 50%
B. 65%
C. 75%
D. 85%
E. 90%

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Joined: 22 May 2016
Posts: 3574
The owners of a traveling televangelist circuit projected a 30 percent  [#permalink]

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01 Jan 2018, 16:01
1
Bunuel wrote:
The owners of a traveling televangelist circuit projected a 30 percent increase in attendance this year over last year. The actual attendance this year was 15 percent less than last year's attendance. Approximately, what percent of the projected attendance was the actual attendance?

A. 50%
B. 65%
C. 75%
D. 85%
E. 90%

Where x = last year's attendance
Projected: 30 percent increase = 1.3x
Actual: 15 percent decrease = .85x

Approximately what percent of the projected attendance was the actual attendance?

$$\frac{.85x}{1.3x} = \frac{85}{130} = \frac{7}{26} \approx{.654} * 100\approx{65}$$ percent

OR:

Let last year's attendance = 100

Projected: a 30 percent increase = 130
Actual: a 15 percent decrease = 85

Approximately what percent of the projected attended was the actual attendance?

$$\frac{85}{130} = \frac{17}{26}$$ * 100 = approximate percent of actual/projected

$$\frac{1}{2}$$ of 26 would be $$\frac{13}{26}$$

$$\frac{17}{26}$$> 50 percent
Eliminate A

$$\frac{2}{3}$$ of 27 (close to 26) = 18 = 66.67 percent of 27
17 is a little less than 18, 26 is a little less than 27
$$\frac{17}{26}$$ will be close to $$\frac{18}{27}$$ = 66.67 percent

65 percent works

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The owners of a traveling televangelist circuit projected a 30 percent   [#permalink] 01 Jan 2018, 16:01
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