Tran has made a plan to help him study for his math exam.
He has broken the material that he has to study into two parts: part A and part B and
has, at most, 2 h every evening over the next week to study.
He wants to spend at least twice as much time studying for part A as for part B.
Show graphically all the possible combinations of time that Tran can study for each part.
Choose three possible combinations. Explain your choices.
To graphically represent the possible combinations of time that Tran can study for each part, we can use a coordinate system with the x-axis representing the time spent on part A and the y-axis representing the time spent on part B.
According to the given conditions, Tran has at most 2 hours every evening for studying, which means the maximum values for both parts A and B will be 2.
To fulfill the requirement of studying at least twice as much time for part A compared to part B, we can start by finding the minimum time for part B and then find the corresponding time for part A.
Let's consider three possible combinations:
1. Part A: 2 hours, Part B: 1 hour
In this combination, Tran spends the maximum time available (2 hours) on part A and half of that time (1 hour) on part B.
2. Part A: 1.5 hours, Part B: 0.75 hours
In this combination, Tran spends 1.5 hours on part A, which is at least twice the time (0.75 hours) spent on part B.
3. Part A: 1 hour, Part B: 0.5 hours
In this combination, Tran spends 1 hour on part A, which is twice the time (0.5 hours) spent on part B.
To graphically represent these combinations, we can plot the points (2, 1), (1.5, 0.75), and (1, 0.5) on the coordinate system, as shown below:
```
| .
2 | .
| .
1.5 | .
| .
1 |______________.
0 | 0.5 1 1.5 2
```
In this way, we can visually represent all the possible combinations of time that Tran can study for each part, where the x-coordinate represents the time spent on part A and the y-coordinate represents the time spent on part B.