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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
85 % pure fruit juice. How many pints of each of the two existing types of drink must be used to make
160 pints of a mixture that is 85 % pure fruit juice?

Respuesta :

now, the percentage figures of say, 70%, 95% and so on, we'll use the decimal format of the, thus 70% is just 70/100 or 0.7 and 95% is just 95/100 or 0.95 and so on

so  [tex]\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentration\\ amount \end{array}\\ &-----&-------&-------\\ \textit{70\% pure}&x&0.7&0.7x\\ \textit{95\% pure}&y&0.95&0.95y\\ -----&-----&-------&-------\\ mixture&160&0.85&(160)(0.85) \end{array}[/tex]

whatever "x" and "y" amounts are, we know, they must add up to 160 pints
thus  x + y = 160

now, whatever the concentrated amount of solute in the mixture, we know they must add up to 160*0.85 or 136

thus   0.7x + 0.95y = 136

thus    [tex]\bf \begin{cases} x+y=160\implies \boxed{y}=160-x\\ 0.7x+0.95y=136\\ ----------\\ 0.7x+0.95\left( \boxed{160-x} \right)=136 \end{cases}[/tex]

solve for "x", to see how much of the 70% pure juice will be needed

what about "y"?  well, y = 160 - x

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