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The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 95% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 220 pints of a mixture that is 95% pure fruit juice?

Sagot :

Answer:

55 from un-pure and 165 from pure

Step-by-step explanation:

to get 220 pints with 95% purity you need a mixture of 209 parts to 11 parts (220 *0.95 and 220 * 0.05)

we call the un-pure mixture a and the pure mixture b

all un-pure parts come from a and b in the following ratios

11 = 0.2a + 0b (each pint of mixture a adds 0.2 pints of unpure stuff and each pint of b adds no unpure stuff)

which we can then solve as:

a = 55

all pure parts come from a and b in the following rations

209 = 0.8a + 1b (each pint of mixture a adds 0.8 pints of pure stuff and each pint of b adds a full pint of the pure stuff)

now we can replace a with 55 (from above)

209 = 44 + b,  and solve to

b = 165

now to double check

55 * (0.8x + 0.2y) + 165x would give you

44x + 11y + 165x, which is

11x + 209y and if you then check the ratio

209 / (209+11) = 0.95 again

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