SOLUTION: Solomon went to the shopping centre to buy supplies for his mathematics project. He spent half of what he had plus R2 in the first shop, half of what he then had plus R1 in the sec

Algebra ->  Equations -> SOLUTION: Solomon went to the shopping centre to buy supplies for his mathematics project. He spent half of what he had plus R2 in the first shop, half of what he then had plus R1 in the sec      Log On


   

Question 1052689: Solomon went to the shopping centre to buy supplies for his mathematics project. He spent half of what he had plus R2 in the first shop, half of what he then had plus R1 in the second shop, half of what he then had plus R1 in the third shop and in the fourth shop half of all he had left. Three rands was left. How much money did he start with?
Found 2 solutions by Fombitz, advanced_Learner:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
He starts with X.
First shop, he spends X%2F2%2B2.
He has X-%28X%2F2%2B2%29=X%2F2-2 left over.
Second shop, he spends %28X%2F2-2%29%2F2%2B1=X%2F4-1%2B1=X%2F4
So he now has X%2F2-2-X%2F4=X%2F4-2 left over.
Third shop, he spends %28X%2F4-2%29%2F2%2B1=X%2F8-1%2B1=X%2F8
So he now has X%2F4-2-X%2F8=X%2F8-2 left
Fourth shop, he spends %28X%2F8-2%29%2F2-1=X%2F16-1%2B1=X%2F16
So now he has, X%2F8-2-X%2F16=X%2F16-2
So now set that equal to 3, and solve for X.
X%2F16-2=3
X%2F16=5
X=80

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
Solomon went to the shopping centre to buy supplies for his mathematics project. He spent half of what he had plus R2 in the first shop, half of what he then had plus R1 in the second shop, half of what he then had plus R1 in the third shop and in the fourth shop half of all he had left. Three rands was left. How much money did he start with?
let
x be what he started with then.
First shop x%2F2%2B2.
remaining x-%28x%2F2%2B2%29=x%2F2-2.
Second shop %28x%2F2-2%29%2F2%2B1=x%2F4-1%2B1=x%2F4
remaining now x%2F2-2-x%2F4=x%2F4-2.
Third shop %28x%2F4-2%29%2F2%2B1=x%2F8-1%2B1=x%2F8
remaining x%2F4-2-x%2F8=x%2F8-2
Fourth shop %28x%2F8-2%29%2F2=x%2F16-1=x%2F16+-1
remaing now , x%2F8-2-x%2F16%2B1=x%2F16-1
x%2F16-1=3
x%2F16=4
x=64
check
64
first shop 32+2 now remaing
30 remaining
second shop 15+1 now remaing
14
third shop 7+1
now remaing 6
fourth shop he spent half of 6 which is 3
and remainder is 3
checks!!