To solve this problem, we need to establish a relationship between the number of true/false questions and the total number of questions based on the percentage given.
(a) Double Number Line:
- We represent the number of true/false questions (49) on one line, and the total number of questions (let's call it "T") on another line.
- We know from the problem that 49 questions correspond to 35% of the total questions. So we can set up ratios.
Here’s a simple representation of a double number line:
| True/False Questions | Total Questions |
|-----------------------|-------------------|
| 0 | 0 |
| 49 | T |
| | 100% |
To find "T," we need to express 35% in fractional terms.
- If 49 questions represent 35%, we can also note that 100% would be the total number of questions. As a number line helps visualize these two comparisons:
- 35% — 49
- 100% — T
(b) Finding Total Number of Questions:
We can create an equation based on the proportion:
\[ 49 = 0.35 \cdot T \]
To solve for \( T \):
\[ T = \frac{49}{0.35} \]
Calculating this gives:
\[ T = \frac{49}{0.35} = 140 \]
Thus, the total number of questions on the exam is 140.
In conclusion:
- (a) The double number line shows the relationship between 49 true/false questions and the total number of questions (T).
- (b) The total number of questions on the exam is 140.
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