Question 1184588: A store is having a sale on jelly beans and almonds. For 8 pounds of jelly beans and 4 pounds of almonds, the total cost is $33. For 3 pounds of jelly beans and 2 pounds of almonds, the total cost is $14. Find the cost for each pound of jelly beans and each pound of almonds.
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
Informally, using logical reasoning....
(1) Double the second purchase to 6 pounds of jelly beans and 4 pounds of almonds for $28.
(2) Compare that to the first purchase of 8 pounds of jelly beans and 4 pounds of almonds for $33.
(3) The difference is 2 more pounds of jelly beans for $5 more, so the cost of each pound of jelly beans is $2.50.
(4) Plug that into either original purchase to find the cost of each pound of almonds is $3.25.
The exact same calculations, using formal algebra....
8j+4a=33 [1]
3j+2a=14 [2]
Double the second equation
6j+4a=28 [3]
Subtract [3] from [1]
2j=5 [4]
j=2.5
Substitute j-2.5 in [1]
8(2.5)+4a=33
20+4a=33
4a=13
a=13/4=3.25
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