SOLUTION: The Delicious Juice Company sells 8-ounce cans of apple juice for 49 cents and 8-ounce cans of apple drink for 25 cents. The company wishes to market and sell cans of juice drink

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Question 182641: The Delicious Juice Company sells 8-ounce cans of apple juice for 49 cents and 8-ounce cans of apple drink for 25 cents. The company wishes to market and sell cans of juice drink for 39 cents that is part juice and part drink. How many ounces of each should be used if the juice drink is to be sold in an 8-ounce can?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a= ounces of 49 cent apple juice needed per 8 ounce can
Let b= ounces of 25 cent apple drink needed per 8 ounce can
given:
(1) a+%2B+b+=+8
The cost per ounce of apple juice is:
49%2F8+=+6.125 cents/oz
The cost per ounce of apple drink is:
25%2F8+=+3.125 cents/oz
-------------------------------------
(2) 6.125a+%2B+3.125b+=+39cents
Multiply both sides of (1) by 3.125
(1) a+%2B+b+=+8
(1) 3.125a+%2B+3.125b+=+25
Subtract (1) from (2)
(2) 6.125a+%2B+3.125b+=+39
(1) -3.125a+-+3.125b+=+-25
(3) 3a+=+14
(3) a+=+4.67 oz
and, since
(1) a+%2B+b+=+8
b+=+8+-+4.67
b+=+3.33 oz
4 2/3 oz of juice and 3 1/3 oz of drink per 8 oz can are needed
check:
(2) 6.125a+%2B+3.125b+=+39
(2) 6.125%2A4.67+%2B+3.125%2A3.33+=+39
(2) 28.583+%2B+10.416+=+39
38.998+=+39 close enough