Certainly! Let's work through each part of the question in detail.
### 1.1.1 Determine the missing values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]
To solve for these missing values, we use the concept of inverse proportionality between the number of workers and the number of days. This relationship can be expressed such that the product of the number of workers and the number of days is a constant value [tex]\( k \)[/tex].
Given:
- 200 workers take 700 days to complete the bridge:
[tex]\[
200 \times 700 = 140000
\][/tex]
Therefore, [tex]\( k = 140000 \)[/tex].
Now, we can use this constant [tex]\( k \)[/tex] to determine the missing values:
1. For [tex]\( A \)[/tex] (days with 70 workers):
[tex]\[
70 \times A = 140000 \implies A = \frac{140000}{70} = 2000
\][/tex]
2. For [tex]\( B \)[/tex] (workers for 400 days):
[tex]\[
B \times 400 = 140000 \implies B = \frac{140000}{400} = 350
\][/tex]
3. For [tex]\( C \)[/tex] (workers for 7000 days):
[tex]\[
C \times 7000 = 140000 \implies C = \frac{140000}{7000} = 20
\][/tex]
So the missing values are:
- [tex]\( A = 2000 \)[/tex]
- [tex]\( B = 350 \)[/tex]
- [tex]\( C = 20 \)[/tex]
### 1.1.2 Complete the sentence
As the number of workers increases, the time to complete the job decreases.
### 1.1.3 How many workers would be needed if the project had to be completed in 50 days?
Using the constant [tex]\( k \)[/tex]:
[tex]\[
\text{Number of workers} \times 50 = 140000 \implies \text{Number of workers} = \frac{140000}{50} = 2800
\][/tex]
So, 2800 workers would be needed to complete the project in 50 days.
### 1.1.4 Complete the statement
The relationship between the number of workers and the number of days to build the bridge is inversely proportional.
This means that as more workers are hired, the time required to complete the job decreases proportionally and vice versa.
