<PRE><B>Question 1210396</B>
&lt;br&gt;
You could possibly do a bunch of work &quot;in the background&quot; to set up this problem using a single variable, but it appears to me that would get quite messy.  So let&#39;s not try to be clever and just go with separate variables for the costs of each of the three items.&lt;br&gt;
He spent 3/8 of his money on the first purchase and 4/5 of the remaining amount on the second purchase.  After spending 3/8 of his money on the first purchase, he had 5/8 of it left, so when he spent 4/5 of his remaining money on the second purchase that was (4/5)(5/8) = 4/8  of his original money.&lt;br&gt;
The cost of each cupcake is 2/3 the cost of a muffin:
m = cost of a muffin
c = cost of a cupcake
c = (2/3)m&lt;br&gt;
The cost of each piece of waffle is $0.20 more than the cost of a cupcake:
w = cost of a piece of waffle
w = c+0.20 = (2/3)m+0.20&lt;br&gt;
Let x be his original amount of money&lt;br&gt;
The cost of 3 cupcakes and 8 muffins was 3/8 of his original money:&lt;br&gt;
{{{3((2/3)m)+8m=(3/8)x}}}
{{{2m+8m=(3/8)x}}}
{{{10m=(3/8)x}}} [1]&lt;br&gt;
The cost of 15 pieces of waffle was 4/8 of his original money:&lt;br&gt;
{{{15((2/3)m+0.20)=(4/8)x}}}
{{{10m+3=(4/8)x}}} [2]&lt;br&gt;
The given information was such that this approach to solving the problem leads to two equations which are easy to solve. Comparing [1] and [2],&lt;br&gt;
{{{3=(1/8)x}}}
{{{24=x}}}&lt;br&gt;
The amount of money he started with was $24.&lt;br&gt;
From [1], the cost of 10 muffins was 3/8 of $24, or $9.  So the cost of each muffin is $9/10 = $0.90.&lt;br&gt;
ANSWER: $0.90&lt;br&gt;
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