# Thread: Want to Figure Out How to Calculate how much you need for decorations? Use this

1. ## Want to Figure Out How to Calculate how much you need for decorations? Use this

It can be tricky to really know how much it costs to buy something like 100+ of one type of path because it always increases. Sometimes you end up paying double or triple the amount for the last one than you did the first. To figure out beforehand how many coins you need to buy all your decorations use this formula.

I believe all the decoration that do increase in price each time you buy one increase by the same amount each time. If it doesn’t increase by the same amount each time then this formula won’t apply

variables (to make it easier to see)
a=#of decorations of a certain type you are buying
c=change in price each time you buy that decoration
b=the price of the decoration currently in your shop
d=product of (a-1) and c
e=quotient of d divided by 2
f=sum of b and e
p=final price

Formula: a{[(a-1)(c)]/2+b} or (1/2ca*2)-(1/2ca)+(ba)
a*2= a(a)

I’ll use the first formula to break down how it works since it is easier to explain, but either works! The second formula is the simplified form and the first one is the factored form.

Breakdown:

First multiple (a-1) and c: This finds the amount of change in price between the first and last decoration.

(a-1)(c)=d

Next divide d by 2: This finds the average change in price from the base price.

d/2=e

Add e to b: This finds the average cost of one decoration.

e+b=f

Lastly multiply f by a: This multiplies the average price of one decoration by the number being bought to give a total amount.

a(f)=p

Example: I want to buy 100 paths that increase by 12 each time and my shop price is 360.

(100-1)(12)=1200-12=1188

1188/2=594

594+360=954

954(100)=95400

Feel free to ask for any questions or further examples if needed!  Reply With Quote

2. Little correction
Formula: a{[(a+1)(c)]/2+b}

for a=1, your formula gives answer 366. This formula gives 372.

for a=100, your formula gives answer 96000. This formula gives 96600.  Reply With Quote

3. Originally Posted by surendrajaipur Little correction
Formula: a{[(a+1)(c)]/2+b}

for a=1, your formula gives answer 366. This formula gives 372.

for a=100, your formula gives answer 96000. This formula gives 96600.
The original formula I gave is actually wrong (I’ve fixed it now) but the one you gave would give the price for the 2nd decoration onward because the formula you gave doesn’t take into account that the first one has no change from the base (the first decoration’s cost would be 360)

The accurate formula would be a{[a-1)(c)]/2+b}

If you sub in 1 for a you would get
1(0/2+360)
1(360)=360

if a=2
2[(2-1)(12)/2+360]
2[(12/2+360]
2(366)
732

Check 360+372=732

if a=5
5[(5-1)(12)/2+360]
5(48/2+360)
5(24+360)
5(384)
1920

Check: 360+372+384+396+408=1920

if a=234
234[(234-1)(12)/2+360]
234[(233)(12)/2+360]
234[1398+360]
234
411,372

Check I used a calculator to add all the values (360, 372, 384, 396…… 3156)  Reply With Quote

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