SOLUTION: Polar Treats sells one-dip ice cream cones for $2.25, two-dip cones for $3.15, and three dip-cones for $3.85. On Saturday, they sold 200 cones for a total of $599.20. Altogether, P

Algebra ->  Graphs -> SOLUTION: Polar Treats sells one-dip ice cream cones for $2.25, two-dip cones for $3.15, and three dip-cones for $3.85. On Saturday, they sold 200 cones for a total of $599.20. Altogether, P      Log On


   



Question 1096313: Polar Treats sells one-dip ice cream cones for $2.25, two-dip cones for $3.15, and three dip-cones for $3.85. On Saturday, they sold 200 cones for a total of $599.20. Altogether, Polar Treats used 380 dips of ice cream. How many of each size cone were sold?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I get it that each cone can have either 1, 2, or 3 dips
Let +a+ = number of 1-dip cones sold on Sat.
Let +b+ = number of 2-dip cones sold on Sat.
Let +c+ = number of 3-dip cones sold on Sat.
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(1) +a+%2B+b+%2B+c+=+200+
(2) +1%2Aa+%2B+2%2Ab+%2B+3%2Ac+=+380+
(3) +2.25a+%2B+3.15b+%2B+3.85c+=+599.2+
----------------------------------------
(3) +225a+%2B+315b+%2B+385c+=+59920+
(3) +45a+%2B+63b+%2B+77c+=+11984+
Multiply both sides of (1) by +45+ and subtract
(1) from (3)
(3) +45a+%2B+63b+%2B+77c+=+11984+
(1) +-45a+-+45b+-+45c+=+-9000+
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+18b+%2B+32c+=+2984+
(4) +9b+%2B+16c+=+1492+
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Subtract (1) from (2)
(2) +a+%2B+2b+%2B+3c+=+380+
(1) +-a+-+b+-+c+=+-200+
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(5) +b+%2B+2c+=+180+
Multiply both sides of (5) by +8+
and subtract (5) from (4)
(4) +9b+%2B+16c+=+1492+
(5) +-8b+-+16c+=+-1440+
---------------------------
+b+=+52+
and
(4) +9%2A52+%2B+16c+=+1492+
(4) +468+%2B+16c+=+1492+
(4) +16c+=+1024+
(4) +c+=+64+
and
(1) +a+%2B+52+%2B+64+=+200+
(1) +a+=+200+-+116+
(1) +a+=+84+
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They sold:
84 1-dip cones
52 2-dip cones
64 3-dip cones
----------------------
check:
(3) +2.25a+%2B+3.15b+%2B+3.85c+=+599.2+
(3) +2.25%2A84+%2B+3.15%2A52+%2B+3.85%2A64+=+599.2+
(3) +189+%2B+163.8+%2B+246.4+=+599.2+
(2) +599.2+=+599.2+