SOLUTION: A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100lb of mixture that will sell for $11.25 per pound. How

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Question 46582This question is from textbook
: A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100lb of mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture? This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x = pounds of $9 beans
y = pounds of $12 beans
together they add up to 100 pounds
x + y = 100
(income from sales of $9 beans) + (income from sales of $12 beans) = total income
total income = (total pounds of mixture) x (price per pound of mixture)
9x+%2B+12y+=+100+%2A+11.25
x+%2B+y+=+100
multiply the 2nd equation by 9 and subtract from the 1st
9x+%2B+12y+=+100+%2A+11.25
9x+%2B+9y+=+900
12y+-+9y+=+1125+-+900
3y+=+225
y+=+75 pounds of $12 beans to be sold
x+%2B+y+=+100
x+%2B+75+=+100
x+=+25 pounds of $9 beans to be sold
check
9x+%2B+12y+=+100+%2A+11.25
9%2A25+%2B+12%2A75+=+1125
225+%2B+900+=+1125
1125+=+1125
OK
x+%2B+y+=+100
25+%2B+75+=+100
100+=+100
OK