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Cooper is working two summer jobs, making \( \$ 12 \) per hour babysitting and \( \$ 16 \) per hour tutoring. Cooper must earn at least \( \$ 240 \) this week. Write an inequality that would represent the possible values for the number of hours babysitting, \( b \), and the number of hours tutoring, \( t \), that Cooper can work in a given week.

Ask by Reid Frank. in the United States
Mar 04,2025

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Answer

The inequality representing Cooper's earnings is \( 12b + 16t \geq 240 \), where \( b \) is the number of hours babysitting and \( t \) is the number of hours tutoring.

Solution

Cooper earns $12 per hour babysitting and $16 per hour tutoring. If he works b hours babysitting and t hours tutoring, his total earnings are given by:   12b + 16t Since he must earn at least $240 this week, the inequality that represents the situation is:   12b + 16t ≥ 240 Additionally, b and t must each be greater than or equal to zero:   b ≥ 0  and  t ≥ 0

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Cooper can earn money from babysitting and tutoring according to the number of hours he works. The earnings from babysitting can be expressed as \( 12b \) and from tutoring as \( 16t \). Since he needs to make at least \$240, the inequality capturing this goal would be: \[ 12b + 16t \geq 240. \] This means that the total amount of money earned from both activities must be greater than or equal to \( \$240 \). Now, to spice things up a bit! Imagine if Cooper took this challenge a step further and decided to track his earnings in a colorful chart, he could visualize how many hours of each job he needs to meet or exceed that magical \( \$240 \) mark! What a fun way to keep score! Another cool scenario could be adding some flexibility! What if he switched one of his jobs for a higher-paying gig? Maybe he discovers a new passion! With each new opportunity, he could easily adjust that inequality and find new paths to meeting or exceeding his earnings goal. Adventure awaits in the world of summer job hustling!

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