SOLUTION: One type of candy cost 60cents a pound while a second costs 80cents a pound. How many pounds of each type must be combined in order to produce 20 pounds of a mixture worth 75cents

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Question 304983: One type of candy cost 60cents a pound while a second costs 80cents a pound. How many pounds of each type must be combined in order to produce 20 pounds of a mixture worth 75cents a pound?
Sat prep. Question.
Ans. 24 nickels

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = pounds of $.60 candy needed
Let b = pounds of $.80 cent candy needed
given:
(1) a+%2B+b+=+20
In words:
(cost of each type of candy used)/(pounds of candy used) = (cost of mixture)/(pounds of mixture)
%28.6a+%2B+.8b%29%2F20+=+.75
.6a+%2B+.8b+=+15
(2) 6a+%2B+8b+=+150
Multiply both sides of (1) by 6 and subtract from (2)
(2) 6a+%2B+8b+=+150
(1) -6a+-+6b+=+120
2b+=+30
b+=+15
and, since
a+%2B+b+=+20
a+=+20+-+15
a+=+5
5 pounds of $.60 candy and 15 pounds of $.80 candy are needed
check:
%28.6%2A5+%2B+.8%2A15%29%2F20+=+.75
%283+%2B+12%29%2F20+=+.75
15%2F20+=+.75
15+=+15
OK