Question 1184464
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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?
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<pre>
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 = {{{(3/5)M}}}       (1)

     b = p + 30             (2)


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


    6(p+30) + 10p = {{{(3/5)M}}},

or

       16p        = {{{(3/5)M}}} - 180.      (3)


From the second statement of the problem,  

        8p   = {{{(1/3)*(2/5)*M}}},          

or

        8p   = {{{(2/15)M}}}.                (4)


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

       {{{(4/15)M}}} = {{{(3/5)M}}} - 180.


It implies

       {{{(3/5)M}}} - {{{(4/15)M}}} = 180

       {{{(9/15)M}}} - {{{(4/15)M}}} = 180

       {{{(5/15)M}}} = 180

       {{{(1/3)M}}} = 180

          M = 180*3 = 540.


<U>ANSWER</U>.  Timothy had $540 dollars, at first.
</pre>

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 .