Answer:
72 pints of the first type
18 pints of the second type
Step-by-step explanation:
See attachment for complete question
Given
[tex]x \to[/tex] first type
[tex]y \to[/tex] second type
Final volume = 90; So:
[tex]x + y = 90[/tex]
From the question, we understand that:
70% of x and 95% of y gives 75% of the fruit juice
This is represented as:
[tex]70\% * x + 95\% * y = 75\%* 90[/tex]
Make x the subject in [tex]x + y = 90[/tex]
[tex]x = 90 - y[/tex]
Substitute: [tex]x = 90 - y[/tex] in [tex]70\% * x + 95\% * y = 75\% * 90[/tex]
[tex]70\% * (90 - y) + 95\% * y = 75\% *90[/tex]
Express percentage as decimal
[tex]0.70 * (90 - y) + 0.95 * y = 0.75 * 90[/tex]
Open brackets
[tex]63 - 0.70y + 0.95y = 67.5[/tex]
Collect like terms
[tex]- 0.70y + 0.95y = 67.5 - 63[/tex]
[tex]0.25y = 4.5[/tex]
Divide both sides by 0.25
[tex]y = \frac{4.5}{0.25}[/tex]
[tex]y = 18[/tex]
Recall that: [tex]x = 90 - y[/tex]
[tex]x = 90 - 18[/tex]
[tex]x = 72[/tex]
