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Answer :
Sure, let's go through the process of understanding the problem and determining the correct inequality step by step.
1. Understand the Variables:
- Let's assume:
- [tex]\( x \)[/tex] represents the manager's number of gigs.
- [tex]\( y \)[/tex] represents the monthly rate.
2. Analyze What the Question is Asking:
- We are looking for the inequality that correctly describes the relationship between the manager's number of gigs, monthly rate, and the last month's earnings.
3. Consider the Given Options:
- [tex]\( x + 20y < 170 \)[/tex]
- [tex]\( x + y < 170 \)[/tex]
- [tex]\( y + 20x > 170 \)[/tex]
- [tex]\( 20x + y \geq 170 \)[/tex]
4. Determine a Logical Relationship:
- Earnings could be based on a fixed rate per gig, a flat monthly rate, or a combination.
- A possible equation can involve a base rate for gigs and an extra amount for each gig.
5. Test Each Option:
- Let's assume that the monthly rate [tex]\( y \)[/tex] might not relate directly to the number of gigs [tex]\( x \)[/tex], which implies a base rate might not apply.
- We focus on the possibility that the last month's earnings need to meet or exceed a certain amount.
6. Choose the Correct Inequality:
- Consider [tex]\( 20x + y \geq 170 \)[/tex]:
- This option suggests that the total of a multiple of the gigs ([tex]\( 20x \)[/tex]) plus the monthly rate ([tex]\( y \)[/tex]) must be at least 170.
- This scenario can logically portray a reasonable situation where each gig contributes a certain amount to the total earnings, which must meet or exceed a minimum threshold.
Therefore, the inequality that relates the manager's number of gigs and monthly rate to the last month's earnings is [tex]\( 20x + y \geq 170 \)[/tex].
1. Understand the Variables:
- Let's assume:
- [tex]\( x \)[/tex] represents the manager's number of gigs.
- [tex]\( y \)[/tex] represents the monthly rate.
2. Analyze What the Question is Asking:
- We are looking for the inequality that correctly describes the relationship between the manager's number of gigs, monthly rate, and the last month's earnings.
3. Consider the Given Options:
- [tex]\( x + 20y < 170 \)[/tex]
- [tex]\( x + y < 170 \)[/tex]
- [tex]\( y + 20x > 170 \)[/tex]
- [tex]\( 20x + y \geq 170 \)[/tex]
4. Determine a Logical Relationship:
- Earnings could be based on a fixed rate per gig, a flat monthly rate, or a combination.
- A possible equation can involve a base rate for gigs and an extra amount for each gig.
5. Test Each Option:
- Let's assume that the monthly rate [tex]\( y \)[/tex] might not relate directly to the number of gigs [tex]\( x \)[/tex], which implies a base rate might not apply.
- We focus on the possibility that the last month's earnings need to meet or exceed a certain amount.
6. Choose the Correct Inequality:
- Consider [tex]\( 20x + y \geq 170 \)[/tex]:
- This option suggests that the total of a multiple of the gigs ([tex]\( 20x \)[/tex]) plus the monthly rate ([tex]\( y \)[/tex]) must be at least 170.
- This scenario can logically portray a reasonable situation where each gig contributes a certain amount to the total earnings, which must meet or exceed a minimum threshold.
Therefore, the inequality that relates the manager's number of gigs and monthly rate to the last month's earnings is [tex]\( 20x + y \geq 170 \)[/tex].
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