Answer :
Sure, let's go through each part of the question step-by-step:
Question 2:
We need to model the scenario: "The 25-mile race time of 172 minutes is no more than three times as long as the winning cyclist's time."
- Let's denote the winning cyclist's time as [tex]\( x \)[/tex].
- The phrase "no more than" translates to "less than or equal to."
- So, 172 minutes is less than or equal to three times the winning cyclist's time.
- This can be written as: [tex]\( 3x \geq 172 \)[/tex].
So, the correct inequality for this scenario is option d: [tex]\( 3x \geq 172 \)[/tex].
Question 3:
Caroline's summer reading log must contain at least seven books.
- Let's denote the number of books Caroline reads as [tex]\( x \)[/tex].
- "At least" means equal to or greater than.
- Therefore, the inequality is: [tex]\( x \geq 7 \)[/tex].
Question 4:
Jenna is saving money for a beach trip. She currently has [tex]$64.75, but her goal is to save more than $[/tex]125. How much more does she need to save?
- Let [tex]\( y \)[/tex] be the additional amount Jenna needs to save.
- Jenna starts with [tex]$64.75, and she wants her total savings \( (64.75 + y) \) to be more than $[/tex]125.
- We have the inequality: [tex]\( 64.75 + y > 125 \)[/tex].
- To find how much more she needs to save, solve for [tex]\( y \)[/tex]:
[tex]\[
y > 125 - 64.75 = 60.25
\][/tex]
Therefore, Jenna needs to save more than $60.25 to reach her goal.
Question 2:
We need to model the scenario: "The 25-mile race time of 172 minutes is no more than three times as long as the winning cyclist's time."
- Let's denote the winning cyclist's time as [tex]\( x \)[/tex].
- The phrase "no more than" translates to "less than or equal to."
- So, 172 minutes is less than or equal to three times the winning cyclist's time.
- This can be written as: [tex]\( 3x \geq 172 \)[/tex].
So, the correct inequality for this scenario is option d: [tex]\( 3x \geq 172 \)[/tex].
Question 3:
Caroline's summer reading log must contain at least seven books.
- Let's denote the number of books Caroline reads as [tex]\( x \)[/tex].
- "At least" means equal to or greater than.
- Therefore, the inequality is: [tex]\( x \geq 7 \)[/tex].
Question 4:
Jenna is saving money for a beach trip. She currently has [tex]$64.75, but her goal is to save more than $[/tex]125. How much more does she need to save?
- Let [tex]\( y \)[/tex] be the additional amount Jenna needs to save.
- Jenna starts with [tex]$64.75, and she wants her total savings \( (64.75 + y) \) to be more than $[/tex]125.
- We have the inequality: [tex]\( 64.75 + y > 125 \)[/tex].
- To find how much more she needs to save, solve for [tex]\( y \)[/tex]:
[tex]\[
y > 125 - 64.75 = 60.25
\][/tex]
Therefore, Jenna needs to save more than $60.25 to reach her goal.
