Question 1200103
<font color=black size=3>
x = number of fancy shirts
7-x = number of plain shirts


<table border = "1" cellpadding = "5">
<tr><td>Type</td><td>Number</td><td>Cost</td></tr>
<tr><td>Fancy</td><td>x</td><td>28x</td></tr>
<tr><td>Plain</td><td>7-x</td><td>15(7-x) = 105-15x</td></tr>
<tr><td>Total</td><td>7</td><td>$131</td></tr>
</table>


Total cost:
fancy + plain = $131
28x + (105-15x) = 131
13x + 105 = 131
13x = 131 - 105
13x = 26
x = 26/13
x = 2


Fancy = x = 2
Plain = 7-x = 7-2 = 5



Check:
1 fancy shirt = $28
2 fancy shirts = 2*$28 = $56
1 plain shirt = $15
5 plain shirts = 5*$15 = $75
2 fancy + 5 plain = $56 + $75 = $131 total
2 fancy + 5 plain = 7 shirts total
The answers are confirmed.


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Another approach:


Let's say all 7 shirts were fancy.
7*28 = 196
She would spend $196


The gap from $131 to $196 is 
196-131 = 65
Her total cost needs to drop by $65 to get to $131


Each time we subtract 1 fancy shirt, and add a plain shirt, we subtract a net cost of $13 (since -28+15 = -13)
Then notice how 13 is a factor of 65
65 = 13*5
This tells us that we need to introduce 5 plain shirts


The 7 fancy shirts will drop to 7-5 = 2 fancy shirts.


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Another approach:


x = number of fancy shirts
y = number of plain shirts


x+y = 7 ... shirt count equation
28x+15y = 131 .... shirt cost equation


Graph those two equations using something like Desmos or GeoGebra. Both are free.


The two equations intersect at (2,5)
Meaning we have x = 2 fancy shirts and y = 5 plain shirts


{{{drawing(400,400,-3,6,-3,6,
graph(400,400,-3,6,-3,6,-100,7-x,(131-28x)/15),
circle(2,5,0.05),
circle(2,5,0.08),
circle(2,5,0.10),
circle(2,5,0.12),
locate(2.1,5.2,"(2,5)")
)}}}

x+y = 7 in green
28x+15y = 131 in blue


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Answers:
<font color=red size=4>2 fancy and 5 plain</font>
</font>