Question 1210396
<pre>
Most tutors, including me, often ignore where it says this:

<font color="red"><b>"Also, if possible, provide a 'check' at the end, so check if the values 
you computed in fact are correct".</b></font>

Nearly always, we skip this check.

If we would read and heed that, then perhaps we might use a different 
method, to make it easier to check.
<font color="blue"><b>
Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins. Then he spent 4/5
of the remaining money on 15 pieces of waffle. Each cupcake cost 2/3 as much as
a muffin. Each piece of waffle cost $0.20 more than a cupcake. What was the 
cost of a muffin?</font></b>

Let T = total money Hakim had at the beginning.
Let C = cost of a cupcake
Let M = cost of a muffin
Let W = cost of a piece of waffle

<font color="blue"><b>Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins.</b></font> 
{{{expr(3/8)T = 3C + 8M}}}

<font color="blue"><b>Then he spent 4/5 of the remaining money</b></font>

which was {{{T - (3C + 8M)}}}

<font color="blue"><b>on 15 pieces of waffle.<b></font> 

{{{expr(4/5)(T-(3C+8M)^"")=15W}}}

<font color="blue"><b>Each cupcake cost 2/3 as much as a muffin.</b></font> 

{{{C=expr(2/3)M}}}

<font color="blue"><b>Each piece of waffle cost $0.20 more than a cupcake.</b></font> 

{{{W = C + 0.20}}}

{{{system(expr(3/8)T = 3C + 8M, expr(4/5)(T-(3C+8M)^""),C=expr(2/3)M, W = C + 0.20)}}}

Go to any of the online solvers for systems of equations

https://www.wolframalpha.com/
https://www.symbolab.com/solver/system-of-equations-calculator
https://cowpi.com/math/systemsolver/4x4.html
https://www.wolframalpha.com/calculators/system-equation-calculator
There are others also.

Type in 

(3/8)T = 3C + 8M,  (4/5)(T-(3C+8M))=15W, C = (2/3)M, W = C+0.20

Press ENTER, get

C = 0.6, M = 0.09, T = 24, W = 0.8 

which we interpret as

C = $0.60, M = $0.90, T = $24.00, W = $0.80.  

<font color="blue"><b>What was the cost of a muffin?</b></font>

$0.90   <--- solved, but not checked.

Now let's check:

<font color="blue"><b>Hakim spent 3/8 of his money on 3 cupcakes and 8 muffins.</font></b>
(3/8)x$24.00 = $9.00

3x$0.60 = $1.80, 8x$0.90 = $7.20, $1.80 + $7.20 = $9.00. 

That checks.

So his remaining money was $24.00 - $9.00 = $15.00

<font color="blue"><b>Then he spent 4/5 of the remaining money</font></b> 

which was (4/5)x$15.00 = $12.00

<font color="blue"><b>on 15 pieces of waffle.</b></font>

15x$0.80 = $12.00 and, indeed, that checks.   

<font color="blue"><b>Each cupcake cost 2/3 as much as a muffin.</font></b> 

$0.60 = (2/3)($0.90)
$0.60 = $0.60, so that checks.

<font color="blue"><b>Each piece of waffle cost $0.20 more than a cupcake.</font></b>

$0.80 = $0.60 + $0.20
$0.80 = $0.80, so that checks. 

Now, as you see, everything checks.

Edwin</pre>