A student spent 60% of her money on books andspent 1/3 of the remainder on notebooks. She had $30 left. How much money did the student have at first?

Question

A student spent 60% of her money on books andspent 1/3 of the remainder on notebooks. She had $30 left. How much money did the student have at first?

Answer 1

Let's add up how much money was spent.

 

First 60% was spent leaving a remainder of %40 percent.    The total amount must be 100%.

 

Next one third of the remainder amount was spent.    So and additional  (1/3) of 40% was spent.   (Remember that of means multiplication.     1/3 * 40% =  40%/3 = 13 1/3 percent.

 

 

So the total amount spent in percent was 60% + 13 1/3 % = 73 1/3%.   The total amount not spent must be

 

100 - 73 1/3% or  26 2/3%.

 

Let A by the total amount of money

 

So 26 2/3%  of  A = 30 dollars.

 

Changing to decimals  0.26667 * A = 30 dollars

 

A = 30/0.26667 = 112.50 dollars.

 

Answer 2

OK, Nicole, this is easier to explain if I could draw you a picture, but I can't, so let's see what we can do here.

 

Let's start with the $30 she has left.  That is 2/3 of the remainder.  This means that it's two parts of the thirds that the remainder was divided into.  If I draw a circle that represents the remainder, divide it into thirds, and two of them equal $30 altogether, that means that one third is $15, so the whole circle is $45.

 

60% = 60/100, which reduces to 3/5.  If she spent 3/5 of her money on books, that means that the $45 is 2/5 of her total, right?

 

Now, draw another circle that represents the total and divide it into fifths.  Two of those equal $45 total, so one equals $22.50.  If each is $22.50, then all five equal $112.50.

 

Hope this helps!