Certainly! Let's go through the problem step-by-step to fully understand how the amounts are calculated.
1. Understanding the Equation:
We start with the equation given:
[tex]\[
y = 50x
\][/tex]
Here, [tex]\( x \)[/tex] represents the number of hours worked, and [tex]\( y \)[/tex] represents the total amount earned based on the number of hours worked.
2. Calculation for Different Values of [tex]\( x \)[/tex]:
- When [tex]\( x = 6 \)[/tex]:
Substitute [tex]\( x = 6 \)[/tex] into the equation:
[tex]\[
y = 50 \times 6 = 300
\][/tex]
Therefore, for 6 hours of work, the amount earned is 300.
- When [tex]\( x = 7 \)[/tex]:
Substitute [tex]\( x = 7 \)[/tex] into the equation:
[tex]\[
y = 50 \times 7 = 350
\][/tex]
Therefore, for 7 hours of work, the amount earned is 350.
- When [tex]\( x = 8 \)[/tex]:
Substitute [tex]\( x = 8 \)[/tex] into the equation:
[tex]\[
y = 50 \times 8 = 400
\][/tex]
Therefore, for 8 hours of work, the amount earned is 400.
3. Summary of Results:
Combining all the results, we have:
- For 6 hours of work ([tex]\( x = 6 \)[/tex]), the amount earned is [tex]\( y = 300 \)[/tex].
- For 7 hours of work ([tex]\( x = 7 \)[/tex]), the amount earned is [tex]\( y = 350 \)[/tex].
- For 8 hours of work ([tex]\( x = 8 \)[/tex]), the amount earned is [tex]\( y = 400 \)[/tex].
Hence, this is how the amounts are determined for each given number of hours worked, according to the provided equation [tex]\( y = 50x \)[/tex].
