SOLUTION: Connie mixed lime juice, lemon juice and water in the ratio 3:6:7 to make 8 liters of drink. How many liters of lime juice did she use?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Connie mixed lime juice, lemon juice and water in the ratio 3:6:7 to make 8 liters of drink. How many liters of lime juice did she use?      Log On


   

Question 806686: Connie mixed lime juice, lemon juice and water in the ratio 3:6:7 to make 8 liters of drink. How many liters of lime juice did she use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let liters of lime juice = +a+
Let liters of lemon juice = +b+
Let liters of water = +c+
-----------------------
(1) +a%2Fb+=+3%2F6+
(2) +b%2Fc+=+6%2F7+
(3) +a+%2B+b+%2B+c+=+8+
--------------------
(1) +6%2Aa+=+3%2Ab+
(1) +a+=+%281%2F2%29%2Ab+
and
(2) +b%2Fc+=+6%2F7+
(2) +7%2Ab+=+6%2Ac+
(2) +c+=+%287%2F6%29%2Ab+
-----------------
Substitute (1) and (2) into (3)
(3) +a+%2B+b+%2B+c+=+8+
(3) +%281%2F2%29%2Ab+%2B+b+%2B+%287%2F6%29%2Ab+=+8+
Multiply both sides by +6+
(3) +3b+%2B+6b+%2B+7b+=+48+
(3) +16b+=+48+
(3) +b+=+3+
and, since
(1) +a+=+%281%2F2%29%2Ab+
(1) +a+=+1.5+
and
(2) +c+=+%287%2F6%29%2Ab+
(2) +c+=+%287%2F6%29%2A3+
(2) +c+=+3.5+
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There are 1.5 liters of lime juice
There are 3 liters of lemon juice
There are 3.5 liters of water
--------------
check:
(3) +a+%2B+b+%2B+c+=+8+
(3) +1.5+%2B+3+%2B+3.5+=+8+
(3) +8+=+8+