Algebra Help. The Royal Fruit Company produces two types of fruit drinks

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 65%

 pure fruit juice, and the second type is 100%

 pure fruit juice. The company is attempting to produce a fruit drink that contains 70%

 pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140

pints of a mixture that is 70%

 pure fruit juice? 

Answer 1

65S+100H = 70(140)

65S + 100(140-S) = 9800

-35S = 9800-14000

S = 4200/35 = 120 pints of 65% fruit juice

H=20 pints of 100% fruit juice

to get 140 pints of 70% fruit juice

70 is so much closer to 65% than to 100% that you know much more of it will be used

70 is 5 away from 65, and 30 away from 100. 65 is 35 away from 100. 70 is 1/7 of the way from 65 to 100.

20 is 1/7 of 140 pints. 20 pints of 100%, 120 of 65% gets 140 of 70%