Thread: Problem solving formula - results don't match

Hi,

My apologies if this is posted in the wrong forum. I am trying to understand the following formula:

Code:

p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]

Its for calculating points earned and I copied it off a games website. I knew what p, k & b were and was trying to find n. My calculations were as follows:

Code:

p=37.95
k=151
b=1

p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
37.95 = 10 * [sqrt(n)/sqrt(151)] * [1 + log(1 + 0.25)]
37.95 = 10 * [sqrt(n)/12.29] * [1 + log(1.25)]
37.95 = 10 * [sqrt(n)/12.29] * [1 + 0.097]
37.95 * 12.29 = 10 * [sqrt(n)/(12.29/12.29)] * [1 + 0.097]                 // I'm not 100% confident this is right. I'm not sure whether they cancel this way
466.406 = 10 * [sqrt(n)] * 1.097
46.6406 = [sqrt(n)] * 1.097                                                // Divide by 10 both sides
42.5165 = sqrt(n)                                                          // Divide by 1.097 both sides
1087 = n                                                                   // Square both sides (rounded to nearest whole number)

When I checked the answer on the site the answer was 1087. So I worked the formula to find p using the 3 variables:

Code:

n=1087
k=151
b=1

p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
p = 10 * [sqrt(1087)/sqrt(151)] * [1 + log(1 + 0.25)]
p = 10 * [32.97/12.29] * [1 + log(1.25)]
p = 10 * [2.68] * [1 + 0.097]
p = 10 * [2.68] * [1.097]
p = 29.3996

The result I was expecting was p = 37.95 which is the result according to the website.

Can someone explain if I am making a mistake somewhere? It's puzzling me since when I worked the formula to find n I got the correct answer. Thanks in advance for your help.

Originally Posted by Fujo23

Hi,

My apologies if this is posted in the wrong forum. I am trying to understand the following formula:

Code:

p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]

Its for calculating points earned and I copied it off a games website. I knew what p, k & b were and was trying to find n. My calculations were as follows:

Code:

p=37.95
k=151
b=1

p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
37.95 = 10 * [sqrt(n)/sqrt(151)] * [1 + log(1 + 0.25)]
37.95 = 10 * [sqrt(n)/12.29] * [1 + log(1.25)]
37.95 = 10 * [sqrt(n)/12.29] * [1 + 0.097]
37.95 * 12.29 = 10 * [sqrt(n)/(12.29/12.29)] * [1 + 0.097]                 // I'm not 100% confident this is right. I'm not sure whether they cancel this way
466.406 = 10 * [sqrt(n)] * 1.097
46.6406 = [sqrt(n)] * 1.097                                                // Divide by 10 both sides
42.5165 = sqrt(n) // Divide by 1.097 both sides
1087 = n                                                                   // Square both sides (rounded to nearest whole number)

When I checked the answer on the site the answer was 1087. So I worked the formula to find p using the 3 variables:

Code:

n=1087
k=151
b=1

p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
p = 10 * [sqrt(1087)/sqrt(151)] * [1 + log(1 + 0.25)]
p = 10 * [32.97/12.29] * [1 + log(1.25)]
p = 10 * [2.68] * [1 + 0.097]
p = 10 * [2.68] * [1.097]
p = 29.3996

The result I was expecting was p = 37.95 which is the result according to the website.

Can someone explain if I am making a mistake somewhere? It's puzzling me since when I worked the formula to find n I got the correct answer. Thanks in advance for your help.

I've marked in blue those values which look a little bit strange.

The first number you marked I divided both sides by 1.097 to remove from the right side

Code:

46.6406 / 1.097 = sqrt(n) * 1.097 / 1.097
42.5165 = sqrt(n)

The second numbers you marked is sqrt of 1087 rounded to two decimal places

Code:

sqrt(1087) = 32.96968304366907316174
sqrt(1087) = 32.97

42.5165 = sqrt(n) OK
n = (42.5165)² = 1807 not 1087

I see my mistake now - I got 1807 the first time I worked it out on paper and when I went to calculate it the other way I switched it to 1087. I even mistyped it when retyping my written work. What an obvious mistake. Thanks that was doing my head in!

It appears that Log is in base 10 and so n=1807.4

Yes it is log base 10 but n is always a whole number while p is rounded up to two decimal places so that's why it doesn't work out to precisely 1807.