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Answer :
To solve this problem, let's break down the information given:
1. Monthly Earnings: The manager earns a monthly rate [tex]\( y \)[/tex] plus [tex]$20 for each show (or gig) booked. The expression for the earnings from the gigs is \( 20x \), where \( x \) represents the number of gigs booked.
2. Total Earnings: We need to find an inequality that shows the relationship between the number of gigs and the monthly rate leading to total earnings of at least \$[/tex]170.
3. Forming the Inequality:
- The total earnings are made up of the monthly rate [tex]\( y \)[/tex] and the earnings from gigs [tex]\( 20x \)[/tex].
- This gives us the total earnings expression: [tex]\( 20x + y \)[/tex].
- Since the earnings are at least \$170, the inequality will be: [tex]\( 20x + y \geq 170 \)[/tex].
So, the inequality that correctly relates the manager's number of gigs and monthly rate to last month's earnings is:
[tex]\[ 20x + y \geq 170 \][/tex]
1. Monthly Earnings: The manager earns a monthly rate [tex]\( y \)[/tex] plus [tex]$20 for each show (or gig) booked. The expression for the earnings from the gigs is \( 20x \), where \( x \) represents the number of gigs booked.
2. Total Earnings: We need to find an inequality that shows the relationship between the number of gigs and the monthly rate leading to total earnings of at least \$[/tex]170.
3. Forming the Inequality:
- The total earnings are made up of the monthly rate [tex]\( y \)[/tex] and the earnings from gigs [tex]\( 20x \)[/tex].
- This gives us the total earnings expression: [tex]\( 20x + y \)[/tex].
- Since the earnings are at least \$170, the inequality will be: [tex]\( 20x + y \geq 170 \)[/tex].
So, the inequality that correctly relates the manager's number of gigs and monthly rate to last month's earnings is:
[tex]\[ 20x + y \geq 170 \][/tex]
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