SOLUTION: A store had a sale on t–shirts, during which they sold 186 t–shirts in three sizes, small, medium and large, and they made $1,892. Smalls sell for $8 each, mediums sell for $10 ea

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Question 401803: A store had a sale on t–shirts, during which they sold 186 t–shirts in three sizes, small, medium
and large, and they made $1,892. Smalls sell for $8 each, mediums sell for $10 each,
and larges sell for $12 each. The total number of smalls and larges sold was 30 more than
the number of mediums sold. How many of each size t–shirt was sold?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
s = number of small t-shirts
m = number of medium t-shirts
l = number of large t-shirts
given:
(1) s+%2B+m+%2B+l+=+186
(2) 8s+%2B+10m+%2B+12l+=+1892
(3) s+%2B+l+=+m+%2B+30
---------------------
This is 3 equations and 3 unknowns, so it's solvable
From (3):
(3) s+-+m+%2B+l+=+30
Now add (1) and (3)
(1) s+%2B+m+%2B+l+=+186
(3) s+-+m+%2B+l+=+30
2s+%2B+2l+=+216
s+%2B+l+=+108
Subtract (3) from this equation:
s+%2B+l+=+108
-s+-+l+=+-m+-+30
0+=+-m+%2B+78
m+=+78
From above,
s+=+108+-+l
Plug this into (2)
(2) 8%2A%28108+-+l%29+%2B+10%2A78+%2B+12l+=+1892
864+-+8l+%2B+780+%2B+12l+=+1892
4l+=+1892+-+780+-+864
4l+=+248
l+=+62
and, also,
s+=+108+-+l
s+=+108+-+62
s+=+46
46 = number of small t-shirts sold
78 = number of medium t-shirts sold
62 = number of large t-shirts sold
check answer:
(2) 8%2A46+%2B+10%2A78+%2B+12%2A62+=+1892
368+%2B+780+%2B+744+=+1892
1892+=+1892
and
(1) 46+%2B+78+%2B+62+=+186
186+=+186
OK