Question 1203277
.
(1) James used 1/4 of his money to buy 3 pencil cases and 7 key chains. 
(2) The cost of each pencil case is 3 times the cost of each key chain. 
(3) He bought some more key chains with 5/6 of his remaining money. 
(4) He spent $30.40 more on all the key chains than on all the pencil cases. 
How much was the cost of one key chain?
~~~~~~~~~~~~~~~~~



I numbered the problem' statements for easy references.



<pre>
Let x be the price of one key chain, in dollars (the unknown value under the problem's question).

Then the price for one pencil case is 3x dollars, according to the problem's statement (2).

The cost of the first purchase (3 pencil cases and 7 key chains) was  3(3x) + 7x = 9x + 7x = 16x.

This cost was 1/4 of his money originally - hence, the original amount of money was  4*(16x) = 64x.


    After his first purchase, the remaining money was {{{(3/4)*64x}}} = 48x.

    James bought additional key chains for {{{(5/6)*48x}}} = 40x dollars.


For key chains, he spent, in all,  7x + 40 = 47x  dollars.

For all pencil cases, he spent 3*(3x) = 9x dollars.

The difference is  47x - 9x = 38x.


From (4), we have this equation for the difference

    38x = 30.40 dollars.


Hence,  x = {{{30.40/38}}} = 0.80 dollars.


<U>ANSWER</U>.  The cost of one key chain is $0.80.
</pre>

Solved.