SOLUTION: There are three types of liquids in a beverage of 700 litres. The ratio of measurement of the first and second liquid is 2:3 and the ratio of measurement of second and third is 4:5

Algebra ->  Proportions  -> Lessons -> SOLUTION: There are three types of liquids in a beverage of 700 litres. The ratio of measurement of the first and second liquid is 2:3 and the ratio of measurement of second and third is 4:5      Log On


   

Question 980127: There are three types of liquids in a beverage of 700 litres. The ratio of measurement of the first and second liquid is 2:3 and the ratio of measurement of second and third is 4:5. Let's workout the ratio in which the first and the second liquid will be mixed so that the ratio of measurement of the three liquids become 6:5:3 in the same beverage.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I picture these liquids in the same container,
but I am able to separate them from eachother
and recombine them in different amounts
-----------------
Let +a = liters of 1st liquid originally
Let +b+ = liters of 2nd liquid originally
Let +c+ = liters of 3rd liquid originally
------------------------------------
(1) +a+%2B+b+%2B+c+=+700+
(2) +a%2Fb+=+2%2F3+
(3) +b%2Fc+=+4%2F5+
-------------------
It sounds like +a+%2B+b+ is going to stay the sme
and also +c+ will stay the same
The new +a+ and +b+ is +a%5B1%5D+ and +b%5B1%5D+
-----------------------------------------------
(4) +a+%2B+b+=+a%5B1%5D+%2B+b%5B1%5D+
(5) +a%5B1%5D%2Fb%5B1%5D+=+6%2F5+
(6) +a%5B1%5D+%2B+b%5B1%5D+%2B+c+=+700+
---------------------------
(2) +a+=+%282%2F3%29%2Ab+
(3) +b+=+%284%2F5%29%2Ac+
--------------------
Substitute (3) into (2)
(2) +a+=+%288%2F15%29%2Ac+
--------------------
(1) (8/15)*c + (4/5)*c + c = 700 }}}
(1) +%288%2F15%29%2Ac+%2B+12%2F15%29%2Ac+%2B+%2815%2F15%29%2Ac+=+700+
(1) +%2835%2F15%29%2Ac+=+700+
(1) +c+=+%283%2F7%29%2A700+
(1) +c+=+300+
and
(3) +b+=+%284%2F5%29%2Ac+
(3) +b+=+%284%2F5%29%2A300+
(3) +b+=+240+
and
(2) +a+=+%288%2F15%29%2Ac+
(2) +a+=+%288%2F15%29%2A300+
(2) +a+=+160+
check:
(1) +a+%2B+b+%2B+c+=+700+
(1) +160+%2B+240+%2B+300+=+700+
(1) +700+=+700+
OK
---------
(4) +a+%2B+b+=+a%5B1%5D+%2B+b%5B1%5D+
(4) +160+%2B+240+=+a%5B1%5D+%2B+b%5B1%5D+
(4) +a%5B1%5D+%2B+b%5B1%5D+=+400+
and
(5) +a%5B1%5D%2Fb%5B1%5D+=+6%2F5+
(5) +a%5B1%5D+=+%286%2F5%29%2Ab%5B1%5D+
Plug this result into (4)
(4) +%286%2F5%29%2Ab%5B1%5D+%2B+b%5B1%5D+=+400+
(4) +%2811%2F5%29%2Ab%5B1%5D+=+400+
(4) +b%5B1%5D+=+2000%2F11+
(4) +b%5B1%5D+=+181.8182+
and
(5) +a%5B1%5D+=+%286%2F5%29%2A%282000%2F11%29+
(5) +a%5B1%5D+=+12000%2F55+
(5) +a%5B1%5D+=+218.1818+
check:
(4) +a%5B1%5D+%2B+b%5B1%5D+=+400+
(4) +181.8182+%2B+218.1818+=+400+
(4) +400+=+400+
OK
check:
(6) +a%5B1%5D+%2B+b%5B1%5D+%2B+c+=+700+
(6) +400+%2B+300+=+700+
(6) +700+=+700+
OK
---------
Finally:
+a%5B1%5D+%2F+b%5B1%5D+=+218.1818%2F181.8182+
+a%5B1%5D%2Fb%5B1%5D+=+1.2+
+1.2+=+12%2F10+
+12%2F10+=+6%2F5+
OK
So, the amounts of the new a and b are:
218.1818 liters and 181.8182 liters