Answer :
Answer:
The inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal can be given as:
[tex]s\leq 15[/tex]
Step-by-step explanation:
The complete question is:
Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.
Solution:
Given:
Darcie wants to crochet a minimum of 3 blankets to donate.
Rate at which she crochet = [tex]\frac{1}{15}[/tex] of a blanket per day.
Maximum number of days she has = 60.
To find the number of days Dancie can skip out of 60 days and still reach her goal.
Let [tex]s[/tex] represent the number of days she can skip.
Number of days left to crochet = [tex](60-s)[/tex] days
At rate of [tex]\frac{1}{15}[/tex] of a blanket per day, number of blankets Dancie can corchet in [tex](60-s)[/tex] days can be given as :
⇒ [tex]\frac{1}{15}(60-s)[/tex]
Simplifying using distribution.
⇒ [tex](\frac{1}{15}.60)-(\frac{1}{15}.s)[/tex]
⇒ [tex]4-\frac{s}{15}[/tex]
Dancie needs to crochet a minimum of 3 blankets to reach her goal.
Thus, the inequality can be given as:
[tex]4-\frac{s}{15}\geq 3[/tex]
Solving the inequality for [tex]s[/tex]
Subtracting 4 both sides.
[tex]4-4-\frac{s}{15}\geq 3-4[/tex]
[tex]-\frac{s}{15}\geq -1[/tex]
Multiplying both sides by -15.
[tex]-15(-\frac{s}{15})\leq -15(-1)[/tex] [On multiplying by a negative number the sign of inequality reverse]
∴ [tex]s\leq 15[/tex]
Thus, Dancie can skip a maximum of 15 days.
Darcie can skip 15 days for volunteering and still be able to crochet 3 blankets in the remaining 45 days.
To find out if Darcie can crochet at least 3 blankets in 60 days while skipping some days for volunteering, let's start with her crocheting rate and the number of days available. Darcie crochets at a rate of [tex]\frac{1}{15}[/tex] of a blanket per day. This means in one day, she can complete [tex]\frac{1}{15}[/tex] of a blanket.
We need to determine the minimum number of days Darcie needs to crochet to complete 3 blankets:
[tex]\text{Number of days needed to crochet 3 blankets} = 3 \times 15 = 45 \text{ days}[/tex]
Darcie has 60 days available in total. If she needs 45 days to crochet 3 blankets, then she can skip:
[tex]60 - 45 = 15 \text{ days}[/tex]
So, Darcie can skip 15 days for volunteering and still be able to crochet 3 blankets in the remaining 45 days.
