The royal fruit company produces two type 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 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 80% pure fruit juice

Answer:66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.Step-by-step explanation:Letx ----> pints of pure fruit juice at 70%y ----> pints of pure fruit juice at 95%we know that[tex]x+y=110[/tex] ----> [tex]x=110-y[/tex] ----> equation ARemember that[tex]70\%=70/100=0.70[/tex][tex]95\%=95/100=0.95[/tex][tex]80\%=80/100=0.80[/tex]so[tex]0.70x+0.95y=0.80(110)[/tex] ----> equation BSolve the system by substitutionsubstitute equation A in equation B[tex]0.70(110-y)+0.95y=0.80(110)[/tex] solve for y[tex]77-0.70y+0.95y=88[/tex] [tex]0.25y=88-77[/tex] [tex]0.25y=11[/tex] [tex]y=44[/tex] Find the value of x[tex]x=110-y[/tex] ---> [tex]x=110-44=66[/tex]therefore66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.