SOLUTION: a blend of coffee has 60% of grade A and 40% of grade B, and is sold at 78 cents a pound. If the blend was 40% grade A and 60% grade B, the price would be 62 cents a pound. find th
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Question 235722: a blend of coffee has 60% of grade A and 40% of grade B, and is sold at 78 cents a pound. If the blend was 40% grade A and 60% grade B, the price would be 62 cents a pound. find the price of grade A per pound Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a blend of coffee has 60% of grade A and 40% of grade B, and is sold at 78 cents a pound.
If the blend was 40% grade A and 60% grade B, the price would be 62 cents a pound.
find the price of grade A per pound
;
Let A = cost of Grade A per pound (in cents)
Let B = cost of Grade B per pound
:
Write an equation for each blend
:
.6A + .4B = 78
.4A + .6B = 62
:
Multiply the 1st equation by 3, multiply the 2nd equation by 2
1.8A + 1.2B = 234
0.8A + 1.2B = 124
---------------------Subtraction eliminates B, find A
1A + 0 = 110
A = 110 cents or $1.10 a lb
:
:
To check our solution, find the cost of B
.6(110) + .4B = 78
66 + .4B = 78
.4B = 78 - 66
.4B = 12
B =
B = 30 cents a lb
;
Check this in the 2nd equation
.4(110) + .6(30) =
44 + 18 = 62; confirms our solution
