Question 1210396
<pre>
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?

Let amount spent, be D, cost of a muffin, M, and cost of a cupcake. C

For the first purchase, we get: {{{(3/8)D = 3C + 8M}}}
                                   <font color = magenta><font size = 4><b>3D = 24C + 64M</font></font></b> ---- Multiplying by LCD, 8 ---- <font color = magenta><font size = 4><b>eq (i)</font></font></b>

For the second purchase, we get:{{{(4/5)(1  -  3/8) * D = 15W}}}
                                {{{(4/5)(5/8)D = 15W}}}
                                {{{(cross(4)/cross(5))(cross(5)/2cross(8))D = 15W}}}
                                <font color = magenta><font size = 4><b>{{{D/2}}} = 15W</font></font></b> ---- <font color = magenta><font size = 4><b>eq (ii)</font></font></b>

Each cupcake cost {{{2/3}}} as much as a muffin, so: <font color = magenta><font size = 4><b>C = {{{(2/3)M = 2M/3}}}</font></font></b> ---- <font color = magenta><font size = 4><b>eq (iii)</font></font></b>

Each piece of waffle cost $0.20 more than a cupcake, so: <font color = magenta><font size = 4><b>W = {{{.2 + 2M/3}}}</font></font></b> ---- <font color = magenta><font size = 4><b>eq (iv)</font></font></b>

{{{D/2 = 15W}}} ------ eq (ii)
{{{D/2 = 15(.2 + 2M/3)}}} ---- Substituting {{{.2 + 2M/3}}} for W, in eq (ii) 
{{{D/2 = 3 + 10M}}}
<font color = magenta><font size = 4><b>D = 6 + 20M</font></font></b> ---- Multiplying by LCD, 2 ---- <font color = magenta><font size = 4><b>eq (v)</font></font></b>


 3D = 24C + 64M ------ eq (i)
{{{3D = 24(2M/3) + 64M}}} --- Substituting {{{2M/3}}} for C, in eq (i) 
3D = 8(2M) + 64M
3D = 16M + 64M
<font color = magenta><font size = 4><b>3D = 80M</font></font></b> ---- <font color = magenta><font size = 4><b>eq (vi)</font></font></b>


   <font color = magenta><font size = 4><b>D =  6 + 20M</font></font></b> ---- <font color = magenta><font size = 4><b>eq (v)</font></font></b>
  <font color = magenta><font size = 4><b>3D =      80M</font></font></b> ---- <font color = magenta><font size = 4><b>eq (vi)</font></font></b>
  <font color = magenta><font size = 4><b>3D = 18 + 60M</font></font></b> ---- Multiplying eq (v) by 3 ---- <font color = magenta><font size = 4><b>eq (vii)</font></font></b>
    0 = - 18 + 20M  --- Subtracting eq (vii) from eq (vi)
- 20M = - 18
<font color = red><font size = 4><b>Cost of a muffin</font></font></b>, or {{{highlight_green(M = (- 18)/(- 20) = 9/10 = highlight("$0.90"))}}}</pre>