College algebra

Question

the royal fruit company produces two types of fruit drinks . the first type of fruit is 20% pure fruit juice and the second type is 45% pure fruit juice. the company is attempting to produce a fruit drink that contains 35% pure fruit juice. how many parts of each of the two existing types of drink must be used to make 160 pints of a mixture that is 35% pure fruit juice.​

Answer 1

35 is 3/5 the way from 20 to 45

3/5 x 160 = 96 pints of 45% and

160-96 = 64 pints of 20% pure fruit juice needed to get 160 pints of 35%

Or the more traditional way to solve this is:

X+Y= 160

X = 160-Y

20X + 45Y = 160(35)

20(160-Y) + 45Y = 160(35)

20(160) - 20Y + 45Y = 160(35)

25Y = 15(160)

Y = 15(160)/25 = 3(160)/5 = 96 pints of 45%

X = 160-96 = 64 pints of 20%