SOLUTION: A 40% dye solution is to be mixed with a dye solution to get 120 liters of a 50% solution. How many liters of the 40% and 70% solutions will be needed?

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In words:
(final liters of dye)/(final liters of solution) = 50%
Let = liters of 40% solution needed
Let = liters of 70% solution needed
given:
(1)
liters of dye in =
liters of dye in =
liters of dye in final solution =
(2)
Multiply both sides of (1) by
Multiply both sides of (2) by
Subtract (1) from (2)
(2)
(1)


and, since



80 liters of 40% solution and 40 liters of 70% solution are needed
check:
(2)
(2)


OK