parking garage

[uptowngirl92]

A particular parking garage is increasing its rates by 15 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob's percentage reduction in the number of days he uses the garage each month?

Looking for easy ways to solve this problem..

[sanjana]

Whats the OA? is it 14%

Confirm and then I will let u know how I solved.

Made a mistake.. Got new days = 87% old days,hece 13% is correct.

[NikolayZ]

Hey there.

We need to introduce 3 variables here.
x- rate.
D- days prior to rate increase
n - days reducted.

so, if the monthly price have to be the same, we have an equation :
xD=1.15*x*(D-n), we need to know n, from this equation. "x" may be terminated

1.15 = 1 15/100, 1 3/20 or 23/20

so,

D-n=D*20/23, -n=(20D/23)-D, n=(3/23)D, or 12/92, would be less then 14% but greater than 13 %.
What is the OA?

[uptowngirl92]

you got it!13%

[life is a test]

alternative way is just to plug in nums:

orig rate =100, new rate = 115
orig days = 2, new days = 200/115 = 40/23

% change = difference/original = (6/23) / 2 = 6/46 -> round it up to 6/48 -> ans is greater than 1/8 since we rounded the denominator up --> ans>12.5%

hope that helps.

[crackgmat007]

I guess the easiest way is to apply inversly prop rule

r * d = amount spent

amount spent is constant. if you increase r by 15%, to maintain the same constant #, we must multiply d by 100/115.

R = r * 115/100

Hence, R * 115/100 * D * 100/115 (must be multiplied to maintain constant) = amount spent

Balance is simple (old - new) / old formula

HTH

[ssuarezo]

Hi:

What about this?
100 -- previous month
115 -- current month

in the current month, I need to save 15, the % to save is 15/115 = 13%

We can't count days 'cause it will change every month (28,29,30-31).

Is this correct? I know this formula is valid for the first month, but, as I see, all the other solutions are valid just for the first month, 13%, am I wrong?

Silvia