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after giving 10% to her sister, she spend 1/3 of what was left on a book and then gave remaining $72 to a animal shelter. how much did Jenny's sister get

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3 Answers

First you need to write a formula.
Jenny took all hr money out of the bank so that is an unknown - call it X
 
10% to her sister is 10% of X = 0.10 X
1/3 to buy a book is 33% of X = 0.33 X  or more exactly  X/3
$72 is all that was left and went to the animal shelter
money in the bank - money to sister - money for book = $72 to the shelter
So:  X - 0.1 X - X/3 = $72
 
Solve the formula  for X and calculate what it is.
After that you can find what 10% of it is.
X - original amount of money
 
0.90 X left after giving 0.10 to her sister.
 
1/3 ( 0.90X )  +72 =0.90 X
 
 2/3 ( 0.90X ) = 72
 
  X = 72/ 0.60 = 120
 
 
I use a 5-step process when working with word problems: (1) read and understand the problem; (2) translate the words into mathematical equations and expressions; (3) check and make sure that I understand what I am solving for; (4) solve the problem; and (5) check to see if the answer makes sense  If not, redo all the steps.
 
Step 1: We are being asked to find out how much money Jenny withdrew from the bank.
 
Step 2: To translate the words into mathematical equations and expressions, we need to know what we do not know.  We do not know how much money Jenny withdrew from the bank.  Let make "x" the amount of money that Jenny withdrew from the bank.  Here are things that we know:
 
x                        (amount of money that Jenny withdrew from the bank)
0.10x                  (amount Jenny gave to her sister)
0.90x                  (amount Jenny kept after giving 10% to her sister)
(0.90x)*(1/3)       (amount Jenny spend on a book)
72=(0.90x)*(2/3) (amount Jenny gave to an animal shelter) 
 
Step 3:  We are solving for "x", which is the amount of money that Jenny withdrew from the bank
 
Step 4:  Solve for "x".  Notice that we have one equation and one unknown [72=(0.90x)*(2/3)]. Therefore, we are able to solve this problem.  When you solve for x, you should receive:
 
x = 72*(3/2)/(.90)
x = 120 dollars   <===== ANSWER
 
Step 5:  To see if this answer makes sense, let's attempt to see if we can get the amount giving to the animal shelter, $72.
 
We know that the Jenny withdrew $120 and gave 10% (or $12) to her sister.  With $108 dollar Jenny kept, she spent 1/3 (or $36) on a book, which left her with $72 to give an animal shelter.  
 
Since we obtain $72, our answer makes sense.