Problem Solving

AAPL wrote:Princeton Review

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 percent greater than the number of people she invited in 2014?

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

OA C

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

AAPL wrote:Princeton Review

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 percent greater than the number of people she invited in 2014?

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

OA C

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