Question
Which situation can be represented by the inequality 3x + 12 < 5x + 8
?
Responses
A Jen has $12 and gets an additional $3 per hour. Frank has $8 and gets an additional $5 per hour. After how many hours will Frank have more money than Jen? Jen has $12 and gets an additional $3 per hour. Frank has $8 and gets an additional $5 per hour. After how many hours will Frank have more money than Jen?
B Doug has walked 12 miles and continues walking 3 miles per hour. Steve has walked 5 miles and continues biking 8 miles per hour. After how many hours will Steve pass Doug? Doug has walked 12 miles and continues walking 3 miles per hour. Steve has walked 5 miles and continues biking 8 miles per hour. After how many hours will Steve pass Doug?
C Wesley has eaten 3 jelly beans and continues eating 12 more per minute. Alex has eaten 5 jelly beans and continues eating 8 more per minute. After how many minutes will Wesley eat more than Alex? Wesley has eaten 3 jelly beans and continues eating 12 more per minute. Alex has eaten 5 jelly beans and continues eating 8 more per minute. After how many minutes will Wesley eat more than Alex?
D Shelly has made 3 necklaces and makes 12 each day. Joanna has made 5 necklaces and makes 8 more each day. After how many days will Joanna make more than Shelly?
?
Responses
A Jen has $12 and gets an additional $3 per hour. Frank has $8 and gets an additional $5 per hour. After how many hours will Frank have more money than Jen? Jen has $12 and gets an additional $3 per hour. Frank has $8 and gets an additional $5 per hour. After how many hours will Frank have more money than Jen?
B Doug has walked 12 miles and continues walking 3 miles per hour. Steve has walked 5 miles and continues biking 8 miles per hour. After how many hours will Steve pass Doug? Doug has walked 12 miles and continues walking 3 miles per hour. Steve has walked 5 miles and continues biking 8 miles per hour. After how many hours will Steve pass Doug?
C Wesley has eaten 3 jelly beans and continues eating 12 more per minute. Alex has eaten 5 jelly beans and continues eating 8 more per minute. After how many minutes will Wesley eat more than Alex? Wesley has eaten 3 jelly beans and continues eating 12 more per minute. Alex has eaten 5 jelly beans and continues eating 8 more per minute. After how many minutes will Wesley eat more than Alex?
D Shelly has made 3 necklaces and makes 12 each day. Joanna has made 5 necklaces and makes 8 more each day. After how many days will Joanna make more than Shelly?
Answers
GPT-4o mini
To determine which situation can be represented by the inequality \(3x + 12 < 5x + 8\), we can analyze each option by identifying the structure of the inequality.
The inequality represents a comparison between two growing quantities over time (where \(x\) represents time). The left side represents the total of one person's amount after \(x\) units of time (hours, minutes, days), and the right side represents another's total after that same time, with the condition that we are looking for when one exceeds the other.
Let's look at the options:
**A.** Jen has $12 and gets an additional $3 per hour. Frank has $8 and gets an additional $5 per hour.
Here, the total amount for Jen after \(x\) hours is represented as \(12 + 3x\) and for Frank as \(8 + 5x\). To determine when Frank has more money than Jen, we set up the inequality as follows:
\[12 + 3x < 8 + 5x\]
This simplifies to \(3x + 12 < 5x + 8\), which matches the inequality we have.
**B.** Doug has walked 12 miles and continues walking 3 miles per hour. Steve has walked 5 miles and continues biking 8 miles per hour.
Doug's total distance after \(x\) hours is \(12 + 3x\), and Steve's distance is \(5 + 8x\). We want to check when Steve surpasses Doug:
\[12 + 3x < 5 + 8x\]
This does not match the inequality \(3x + 12 < 5x + 8\).
**C.** Wesley has eaten 3 jelly beans and continues eating 12 more per minute. Alex has eaten 5 jelly beans and continues eating 8 more per minute.
Wesley's total after \(x\) minutes is \(3 + 12x\) and Alex's is \(5 + 8x\). We want to set up the inequality for when Wesley surpasses Alex:
\[3 + 12x < 5 + 8x\]
This does not match our original inequality.
**D.** Shelly has made 3 necklaces and makes 12 each day. Joanna has made 5 necklaces and makes 8 more each day.
Shelly's total after \(x\) days is \(3 + 12x\) and Joanna's is \(5 + 8x\). We need to determine when Joanna surpasses Shelly:
\[3 + 12x < 5 + 8x\]
This inequality rearranges to \(12x + 3 < 8x + 5\), which also does not match.
After examining all the options, **the correct situation that can be represented by the inequality \(3x + 12 < 5x + 8\) is A**, with Jen and Frank's earnings.
The inequality represents a comparison between two growing quantities over time (where \(x\) represents time). The left side represents the total of one person's amount after \(x\) units of time (hours, minutes, days), and the right side represents another's total after that same time, with the condition that we are looking for when one exceeds the other.
Let's look at the options:
**A.** Jen has $12 and gets an additional $3 per hour. Frank has $8 and gets an additional $5 per hour.
Here, the total amount for Jen after \(x\) hours is represented as \(12 + 3x\) and for Frank as \(8 + 5x\). To determine when Frank has more money than Jen, we set up the inequality as follows:
\[12 + 3x < 8 + 5x\]
This simplifies to \(3x + 12 < 5x + 8\), which matches the inequality we have.
**B.** Doug has walked 12 miles and continues walking 3 miles per hour. Steve has walked 5 miles and continues biking 8 miles per hour.
Doug's total distance after \(x\) hours is \(12 + 3x\), and Steve's distance is \(5 + 8x\). We want to check when Steve surpasses Doug:
\[12 + 3x < 5 + 8x\]
This does not match the inequality \(3x + 12 < 5x + 8\).
**C.** Wesley has eaten 3 jelly beans and continues eating 12 more per minute. Alex has eaten 5 jelly beans and continues eating 8 more per minute.
Wesley's total after \(x\) minutes is \(3 + 12x\) and Alex's is \(5 + 8x\). We want to set up the inequality for when Wesley surpasses Alex:
\[3 + 12x < 5 + 8x\]
This does not match our original inequality.
**D.** Shelly has made 3 necklaces and makes 12 each day. Joanna has made 5 necklaces and makes 8 more each day.
Shelly's total after \(x\) days is \(3 + 12x\) and Joanna's is \(5 + 8x\). We need to determine when Joanna surpasses Shelly:
\[3 + 12x < 5 + 8x\]
This inequality rearranges to \(12x + 3 < 8x + 5\), which also does not match.
After examining all the options, **the correct situation that can be represented by the inequality \(3x + 12 < 5x + 8\) is A**, with Jen and Frank's earnings.