SOLUTION: An ice cream shop sells sundaes in three size: small, 89¢; MEDIUM, $1.19; and large, $1.39. On a recent day, Robert sold 52 sundaes. He sold two more than twice as many as mediums

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Question 1082706: An ice cream shop sells sundaes in three size: small, 89¢; MEDIUM, $1.19; and large, $1.39. On a recent day, Robert sold 52 sundaes. He sold two more than twice as many as mediums as larges. If $58.98 was the total income from selling the sundaes, how many of each size did he sell?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of small sizes he sold
Let +b+ = number of medium sizes he sold
Let +c+ = number of large sizes he sold
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There are 3 unknowns, so 3 equations
are needed to solve
(1) +a+%2B+b+%2B+c+=+52+
(2) +b+=+2c+%2B+2+
(3) +.89a+%2B+1.19b+%2B+1.39c+=+58.98+
-----------------------------------------
(3) +89a+%2B+119b+%2B+139c+=+5898+
plug 2 into 1
(1) +a+%2B+%28+2c+%2B+2+%29+%2B+c+=+52+
(1) +a+=+50+-+3c+
Plug (1) and (2) into (3)
(3) +89%2A%28+50+-+3c+%29+%2B+119%2A%28+2c+%2B+2+%29+%2B+139c+=+5898+
(3) +4450+-+267c+%2B+238c+%2B+238+%2B+139c+=+5898+
(3) +377c+-+267c+=+5898+-+4450+-+238+
(3) +110c+=+1210+
(3) +c+=+11+
and
(2) +b+=+2c+%2B+2+
(2) +b+=+2%2A11+%2B+2+
(2) +b+=+24+
and
(1) +a+=+50+-+3c+
(1) +a+=+50+-+3%2A11+
(1) +a+=+17+
----------------------
17 = number of small sizes he sold
24 = number of medium sizes he sold
11 = number of large sizes he sold
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check answer:
(3) +.89a+%2B+1.19b+%2B+1.39c+=+58.98+
(3) +.89%2A17+%2B+1.19%2A24+%2B+1.39%2A11+=+58.98+
(3) +15.13+%2B+28.56+%2B+15.29+=+58.98+
(3) +58.98+=+58.98+
OK
You can check (1) and (2)