In 2015, Ashley invited 12% more people to her annual

BTGmoderatorDC wrote:In 2015, Ashley invited 12% more people to her annual celebration than she did in 2014. If every subsequent year Ashley invites 10% more people to her annual celebration than she did the year before, then the number of people she invites in 2017 is approximately what percentage greater than the number of people she invited in 2014 ?

A. 22%
B. 32%
C. 35%
D. 48%
E. 135%

OA C

Source: Princeton Review

Say the number of people Ashley invited in 2014 was 100. Thus, she invited 100 + 12% of 100 = 112 people in 2015. Thus, she invited 112 + 10% of 112 = appx 123 people in 2016. And finally, she invited 123 + 10% of 123 = appx 135 people in 2017.

Thus, the number of people she invites in 2017 is approximately 35 percent greater than the number of people she invited in 2014.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote:In 2015, Ashley invited 12% more people to her annual celebration than she did in 2014. If every subsequent year Ashley invites 10% more people to her annual celebration than she did the year before, then the number of people she invites in 2017 is approximately what percentage greater than the number of people she invited in 2014 ?

A. 22%
B. 32%
C. 35%
D. 48%
E. 135%

OA C

Source: Princeton Review

We can let n = the number of people Ashley invited in 2014. So we have:

2015 = 1.12n

2016 = 1.12n x 1.1

2017 = 1.12n x 1.1 x 1.1

So the percent increase is:

((1.12n x 1.1 x 1.1) - n)/n x 100

(1.12 x 1.1 x 1.1 - 1) x 100 ≈ 0.35 x 100 = 35%

Alternate Solution:

Let’s assume that Ashley invited 100 people to the celebration in 2014. Thus, in 2015, she invited 1.12 x 100 = 112 people. In 2016 she invited 1.1 x 112 ≈ 123 people, and in 2017 she invited 1.1 x 123 ≈ 135 people.

Using the percent change formula for the years 2017 and 2014, we have:

(135 - 100)/ 100 x 100% = 35%

Answer: C