For the 1st fruit drink, 220 pints will be used
For the 2nd fruit drink, 40 pints will be used
Explanation:
1st type has concentration = 35% = 0.35
2nd type has concentration = 100% = 1
let the amount for the 35% pure fruit = x
Total amount of fruit juice to be made = 260
amount for the 35% pure fruit + amount for the 100% pure fruit = 260
amount for the 100% pure fruit = 260 - x
concentration of mixture = 45% = 0.45
Amount = 260 pints
concentration for the 1st type (amount) + concentration of the 2nd type (amount) = concentration of mixture (amount)
[tex]0.35(x)\text{ + 1}(260\text{ - x})\text{ = 0.45}(260)[/tex]
Solve for x:
[tex]\begin{gathered} 0.35x\text{ + 260 - x = 117} \\ 0.35x\text{ - x + 260 = 117} \\ -0.65x\text{ + 260 = 117} \\ -0.65x\text{ = 117 - 260} \end{gathered}[/tex][tex]\begin{gathered} -0.65x\text{ = - 143} \\ divide\text{ both sides by -0.65:} \\ \frac{-0.65x}{-0.65}\text{ = }\frac{-143}{-0.65} \\ x\text{ = 220} \\ \\ Amount\text{ for 35\% pure fruit = 220pints} \end{gathered}[/tex]
Amount for the 100% pure fruit = 260 - x
Amount for the 100% pure fruit = 260 - 220 = 40 pints
For the 1st fruit drink, 220 pints will be used and for the 2nd fruit drink, 40 pints will be used
