SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting t

Algebra ->  College  -> Linear Algebra -> SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting t      Log On


   

Question 1140981: The Royal Fruit Company produces two types of fruit drinks. The first type is
70%
pure fruit juice, and the second type is
95%
pure fruit juice. The company is attempting to produce a fruit drink that contains
75%
pure fruit juice. How many pints of each of the two existing types of drink must be used to make
70
pints of a mixture that is
75%
pure fruit juice?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
AVAILABLE
70% pure fruitjuice
95% pure fruitjuice

WANT RESULT
70 pints of 75% fruitjuice

Find HOW MUCH OF EACH?

ASSIGN VARIABLES
L, 70%
H, 95%
T, 75%
M, 70 pints
u, how much of 70%
v, how much of 95%

ONE OR TWO EQUATIONS
system%28u%2Bv=M%2CuL%2BvH=TM%29

For a single equation in the unknown variable v,
uL%2BHv=TM
highlight_green%28L%28M-v%29%2BHv=TM%29
LM-Lv%2BHv=TM
Hv-Lv=TM-LM
v%28H-L%29=TM-LM
highlight%28v=%28TM-LM%29%2F%28H-L%29%29-------substitute the given known values and evaluate v. Substitute in other material sum equation to evaluate u.