High School

Darcie wants to crochet a minimum of 333 blankets to donate to a homeless shelter. She crochets at a rate of \(\dfrac{1}{15}\) of a blanket per day. She has 60 days until she wants to donate the blankets, but she also wants to skip crocheting on some days to volunteer in other ways.

How many days can Darcie skip crocheting while still meeting her goal?

Answer :

Answer:

she can skip 15 days and she will take 45 days for this work

Step-by-step explanation:

total blankets to crochet =3

speed of work per day = 1/15 blanket per day

total time in days she have = 60 days

No of days she had=60

number of days required to complete the work = ?

so 1/15 blanket she made = 1 day

1 blanket she made = 1 x 1/15

3 blanket she made =1 x 1/15 x 3 = 15 x 3 = 45 days

So she will do it 45 days.

days can be skipped = 60-45=15 days

Darcie must crochet every day to donate 333 blankets in 60 days, no days can be skipped.

To calculate how many days Darcie can skip crocheting while still reaching her goal of 333 blankets donated, we can set up an equation.

Let [tex]\( x \)[/tex] be the number of days Darcie skips crocheting.

The total number of blankets Darcie crochets in [tex]\( 60 \) days is \( \dfrac{1}{15} \times 60 = 4 \)[/tex] blankets.

So, the equation becomes:

[tex]\[ 4 + \left( \dfrac{1}{15} \times (60 - x) \right) \geq 333 \][/tex]

Let's solve for [tex]\( x \):[/tex]

[tex]\[ 4 + \left( \dfrac{1}{15} \times (60 - x) \right) \geq 333 \][/tex]

[tex]\[ \dfrac{60 - x}{15} \geq 329 \][/tex]

[tex]\[ 60 - x \geq 329 \times 15 \][/tex]

[tex]\[ 60 - x \geq 4935 \][/tex]

[tex]\[ x \leq 60 - 4935 \][/tex]

[tex]\[ x \leq -4875 \][/tex]

[tex]\[ x \leq -4875 \][/tex]

However, [tex]\( x \)[/tex] represents the number of days Darcie can skip crocheting, so it cannot be negative. This means Darcie cannot skip negative 4875 days of crocheting.

In practical terms, Darcie needs to crochet every day or as close to every day as possible to reach her goal of 333 blankets in 60 days.