Raisins sell fro $4.50/lb and bran flakes sell for $2.80/lb. how many pounds of raisins must be mixed with 12 pounds of bran flakes to get a mixture that sells for $3.14/lb ?

The quantity of raisins that will be mix with 12 pounds of bran flake to get mixture  is 3 pounds .  

Step-by-step explanation:

Given as :

The cost of Raisins = $ 4.50 per lb

The cost of bran flakes = $ 2.80 per lb

The quantity of bran flakes = 12 pounds

The cost of mixture = $ 3.14 per lb

Let The quantity of raisins added to the mixture = x pounds

Now, According to question

The cost of Raisins × The quantity of raisins + The cost of bran flakes × The quantity of bran flakes = The quantity of mixture × The cost of mixture

Or, ( $ 4.50 per lb  × x pounds ) + (  $ 2.80 per lb × 12 pounds ) = (  $ 3.14 per lb × ( x pounds + 12 pounds ) )

Or,  ( $ 4.50 per lb  × x pounds ) + 33.6  = ( $ 3.14 per lb × x ) + 37.68

or, ( $ 4.50 per lb  × x pounds )  -  ( $ 3.14 per lb × x ) = 37.68 - 33.60

Or, 1.36 x  = 4.08

∴  x = 3 pounds

Hence The quantity of raisins that will be mix with 12 pounds of bran flake to get mixture  is 3 pounds .   Answer

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.