SOLUTION: Timothy spent 3/5 of his money on 6 bolsters and 10 pillows. He spent 1/3 of his remaining money on 8 more pillows. Each bolster cost $30 more than a pillow. How much money did Tim

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Timothy spent 3/5 of his money on 6 bolsters and 10 pillows. He spent 1/3 of his remaining money on 8 more pillows. Each bolster cost $30 more than a pillow. How much money did Tim      Log On


   

Question 1184464: Timothy spent 3/5 of his money on 6 bolsters and 10 pillows. He spent 1/3 of his remaining money on 8 more pillows. Each bolster cost $30 more than a pillow. How much money did Timothy have at first?
Found 2 solutions by ikleyn, 54929:
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.
Timothy spent 3/5 of his money on 6 bolsters and 10 pillows.
He spent 1/3 of his remaining money on 8 more pillows.
Each bolster cost $30 more than a pillow.
How much money did Timothy have at first?
~~~~~~~~~~~~~~ 

Let b = price for a bolster; p = price for a pillow and M = "How much money did Timothy have at first".


From the first and the third statements of the problem, we have these equations


    6b + 10p = %283%2F5%29M       (1)

     b = p + 30             (2)


Substitute (2) into (1).  You will get


    6(p+30) + 10p = %283%2F5%29M,

or

       16p        = %283%2F5%29M - 180.      (3)


From the second statement of the problem,  

        8p   = %281%2F3%29%2A%282%2F5%29%2AM,          

or

        8p   = %282%2F15%29M.                (4)


From (4) and (3), you get this equation for M

       %284%2F15%29M = %283%2F5%29M - 180.


It implies

       %283%2F5%29M - %284%2F15%29M = 180

       %289%2F15%29M - %284%2F15%29M = 180

       %285%2F15%29M = 180

       %281%2F3%29M = 180

          M = 180*3 = 540.


ANSWER.  Timothy had $540 dollars, at first.

The problem can be solved in different ways, including the ways of using two or three unknowns.
My goal in this post was to reduce the problem to one single equation for one unknown M .



Answer by 54929(12) About Me  (Show Source):
You can put this solution on YOUR website!
According to the given, we can define that a pillow cost x, so a bolster cost x + 30, and Timothy have $y at first, so we have.
3%2F5y = b (x+30) + 10x (1)
{
(1-3/5)*1/3y = 8x (2)
(2) => y = 60x Put y = 60x into (1)
3%2F5*60x = (x + 180 + 10x)
36x - 16x + 180
20x = 180
x = 9
So y = 60 * 9 = $540
So Timothy have $540 at first.