Tran has made a plan to help him study for his math exam.
He has broken down the material that he has to study into two parts: part A and part B and has, at most, 2 hours
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.
Great !
To graphically represent the possible combinations of time that Tran can study for each part, we can use a coordinate grid.
Let's assume that the horizontal axis represents the time spent studying for part A, and the vertical axis represents the time spent studying for part B.
Based on the given conditions:
1. Tran has at most 2 hours every evening over the next week to study.
2. He wants to spend at least twice as much time studying for part A as for part B.
We can start by plotting the minimum and maximum values on the graph.
Minimum values:
Part A: 0 hours
Part B: 0 hours
Maximum values:
Part A: 2 hours
Part B: 1 hour (assuming Tran spends half of the available time on part B)
The graph would look like this:
|
2 +-----------------+
| |
| |
| |
| |
1 +-----------------+
|
|
|
+-----------------+
0 1
The points where the lines intersect (0, 0), (2, 0), and (2, 1) represent the possible combinations of time that Tran can study for each part.
For example:
(0,0) means Tran doesn't study for either part.
(2,0) means Tran spends all 2 hours studying for part A and doesn't study for part B.
(2,1) means Tran spends all 2 hours studying for part A and 1 hour studying for part B.
These points represent all the possible combinations of time that Tran can study for each part, within the given conditions.
To help Tran visualize the different combinations of study time for part A and part B, we can create a graph known as a coordinate plane. The x-axis will represent the study time for part A, while the y-axis will represent the study time for part B.
Since Tran wants to spend at least twice as much time studying for part A as for part B, we can start by assuming that Tran spends 1 hour studying for part B. Therefore, the minimum study time for part A would be 2 hours (twice as much as part B).
Here's a graphical representation of the possible combinations of study time for Tran:
```
Part A (hours) Part B (hours)
------------------------------
2 1
3 1
4 1
5 1
. .
. .
. .
```
As Tran has a maximum of 2 hours every evening over the next week to study, we can limit our graph to a maximum of 2 hours for both part A and part B.
```
Part A (hours) Part B (hours)
------------------------------
2 1
2 0
1 0
0 0
```
In the graph above, the combination (2,1) represents spending 2 hours studying for part A and 1 hour studying for part B. (2,0) means spending 2 hours studying for part A but no time for part B because Tran wants to spend at least twice as much time on part A as on part B.
By plotting all the possible combinations on the graph, we can see the range of study time options available to Tran for each part.
draw a bar graph, with the bars of height 2 or less for each night
shade in each bar with 2 colors for a and b, making sure that b is no more than 1/3 of the full height. Then shade in the "a" part, which must be at least twice as tall as the "b" part.