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Answer :
Sure, let's go through the problem step by step to help Darcie determine how many days she can skip crocheting while still meeting her goal of making at least 3 blankets.
1. Understand Darcie's Rate of Work:
- Darcie crochets at a rate of [tex]\(\frac{1}{15}\)[/tex] of a blanket per day. This means she can complete 1 full blanket every 15 days.
2. Identify Total Time Available:
- Darcie has a total of 60 days to complete her blankets.
3. Set Up the Problem:
- Let's say [tex]\(s\)[/tex] is the number of days Darcie decides to skip crocheting. Therefore, the days she actually spends crocheting are [tex]\(60 - s\)[/tex].
4. Write an Expression for Blankets Produced:
- The number of blankets Darcie can crochet in the days she works is given by the product of her rate and the number of days worked:
[tex]\[
\text{Blankets produced} = \frac{1}{15} \times (60 - s)
\][/tex]
5. Set Up the Inequality:
- We need this expression to be at least 3 since Darcie wants to crochet a minimum of 3 blankets:
[tex]\[
\frac{1}{15} \times (60 - s) \geq 3
\][/tex]
6. Solve the Inequality:
- First, multiply both sides of the inequality by 15 to eliminate the fraction:
[tex]\[
60 - s \geq 3 \times 15
\][/tex]
- Calculate the right side:
[tex]\[
60 - s \geq 45
\][/tex]
7. Isolate [tex]\(s\)[/tex]:
- Subtract 45 from both sides to solve for [tex]\(s\)[/tex]:
[tex]\[
60 - 45 \geq s
\][/tex]
- Simplify:
[tex]\[
15 \geq s
\][/tex]
8. Conclusion:
- Darcie can skip up to 15 days of crocheting and still meet her goal of making at least 3 blankets.
Therefore, the maximum number of days Darcie can skip crocheting is 15 days. This ensures she still meets her goal of completing a minimum of 3 blankets within the 60-day period.
1. Understand Darcie's Rate of Work:
- Darcie crochets at a rate of [tex]\(\frac{1}{15}\)[/tex] of a blanket per day. This means she can complete 1 full blanket every 15 days.
2. Identify Total Time Available:
- Darcie has a total of 60 days to complete her blankets.
3. Set Up the Problem:
- Let's say [tex]\(s\)[/tex] is the number of days Darcie decides to skip crocheting. Therefore, the days she actually spends crocheting are [tex]\(60 - s\)[/tex].
4. Write an Expression for Blankets Produced:
- The number of blankets Darcie can crochet in the days she works is given by the product of her rate and the number of days worked:
[tex]\[
\text{Blankets produced} = \frac{1}{15} \times (60 - s)
\][/tex]
5. Set Up the Inequality:
- We need this expression to be at least 3 since Darcie wants to crochet a minimum of 3 blankets:
[tex]\[
\frac{1}{15} \times (60 - s) \geq 3
\][/tex]
6. Solve the Inequality:
- First, multiply both sides of the inequality by 15 to eliminate the fraction:
[tex]\[
60 - s \geq 3 \times 15
\][/tex]
- Calculate the right side:
[tex]\[
60 - s \geq 45
\][/tex]
7. Isolate [tex]\(s\)[/tex]:
- Subtract 45 from both sides to solve for [tex]\(s\)[/tex]:
[tex]\[
60 - 45 \geq s
\][/tex]
- Simplify:
[tex]\[
15 \geq s
\][/tex]
8. Conclusion:
- Darcie can skip up to 15 days of crocheting and still meet her goal of making at least 3 blankets.
Therefore, the maximum number of days Darcie can skip crocheting is 15 days. This ensures she still meets her goal of completing a minimum of 3 blankets within the 60-day period.
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