Question
Name: Write an inequality to represent each situation: 1. Last week's profits were at most \( \$ 50.00 \). 2. The next town is at least 60 miles away. 3. The maximum speed is 55 mph . 4. He charges less than \( \$ 400 \) to paint a car. 5. The minimum wage is \( \$ .950 \) 6. There are more than 50 bugs on the bush. 7. The cost of snacks was greater than \( \$ 12 \). 8. Kylie pays no less than \( \$ 20 \) for her nails. 9. Fewer than 30 people attended the trip. 10. Mom said no more than 10 people at my party.
Ask by Ross Weston. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1. \( p \leq 50 \)
2. \( d \geq 60 \)
3. \( s \leq 55 \)
4. \( c < 400 \)
5. \( w \geq 0.950 \)
6. \( b > 50 \)
7. \( c > 12 \)
8. \( p \geq 20 \)
9. \( a < 30 \)
10. \( p \leq 10 \)
Solution
Let's write inequalities for each of the situations described:
1. Last week's profits were at most \( \$ 50.00 \):
\[
p \leq 50
\]
where \( p \) represents last week's profits.
2. The next town is at least 60 miles away:
\[
d \geq 60
\]
where \( d \) represents the distance to the next town.
3. The maximum speed is 55 mph:
\[
s \leq 55
\]
where \( s \) represents the speed.
4. He charges less than \( \$ 400 \) to paint a car:
\[
c < 400
\]
where \( c \) represents the charge to paint a car.
5. The minimum wage is \( \$ 0.950 \):
\[
w \geq 0.950
\]
where \( w \) represents the minimum wage.
6. There are more than 50 bugs on the bush:
\[
b > 50
\]
where \( b \) represents the number of bugs.
7. The cost of snacks was greater than \( \$ 12 \):
\[
c > 12
\]
where \( c \) represents the cost of snacks.
8. Kylie pays no less than \( \$ 20 \) for her nails:
\[
p \geq 20
\]
where \( p \) represents the amount Kylie pays for her nails.
9. Fewer than 30 people attended the trip:
\[
a < 30
\]
where \( a \) represents the number of people who attended the trip.
10. Mom said no more than 10 people at my party:
\[
p \leq 10
\]
where \( p \) represents the number of people at the party.
These inequalities represent the conditions given in each situation.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
Last week's profits can be represented by the inequality \( P \leq 50 \), where \( P \) stands for profits. This means that profits did not exceed \( \$50.00 \), ensuring we keep things within budget, or "at most" that dollar limit! For the distance to the next town, we can write the inequality \( D \geq 60 \), indicating that the distance \( D \) is no less than 60 miles. So pack your bags and fuel up, because your road trip is going to be a bit of a trek!
