Silvia wants to mix a 20% apple juice drink with pure apple juice to make 4 L of a juice drink that is 80% apple juice. How much
1 answer:
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Answer:
3 liters
Step-by-step explanation:
There's a simple and effective "visual" way to solve mixture problems that makes short work of this.
In the attached, the concentrations of the contributors are listed on the left. It can work well to put the largest contributor on top (though that is not strictly necessary). The target concentration is put in the middle between them, and the differences along the diagonals are computed.
The diagonal differences are reduced to lowest terms as a ratio in the right-hand column. These numbers can be compared to the problem statement to see how they relate.
In this case, the total is 4 L of juice, and the total of the ratio units is 4. Then the ratio units are the number of liters of the corresponding contributor:
- 3 L of 100% juice
- 1 L of 20% juice
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Answer:
(a) 16 students failed for exactly two of the three reasons.
(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.
(c) 14 students failed because of exactly one of the three reasons.
(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.
Step-by-step explanation:
We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.
As shown in the diagram attached below, a Venn diagram represents the situation given in the question;
In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.
7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.
6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.
3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.
2 in red color represents the number of students who failed only due to poor attendance.
8 in red color represents the number of students who failed only due to not studying.
4 in red color represents the number of students who failed only due to not turning in assignments.
(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.
(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.
(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.
(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.
