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Digiron
1 month ago
8

Alley bought 1 pound of potatoes costing $4 from a local grocery store last week. Her final bill included an additional sales ta

x 8%. The next week alley found that the price for a pound of potatoes had gone up to $6. What is the percentage increase in the cost of a pound of potatoes, including the sales tax?
Mathematics
2 answers:
AnnZ [12.3K]1 month ago
8 0
$6.00 multiplied by 8% equals $6.48

this is the answer. hope this helps
Svet_ta [12.7K]1 month ago
4 0

Answer: 54%

Step-by-step explanation:

Provided information: The price for 1 pound of potatoes at a local grocery store last week was $4.

The total cost for 1 pound of potatoes last week, including an 8% sales tax, was $4 + 8% of $4.

=4+0.08\times4=4+0.32=\$4.32

This week, the price for 1 pound of potatoes at the grocery store is $6.

The total price for 1 pound of potatoes this week, after 8% tax, is $6 + 8% of $6.

=6+0.08\times6=6+0.48=\$6.48

The formula to calculate the percentage increase in the price of a pound of potatoes, factoring in sales tax, is as follows:

P=\frac{\text{ increase in cost}}{\text{cost last week}}\times100\\\\\Rioghtarrow\ P=\frac{6.48-4.32}{4}\times100\\\\\Rightarrow\ P=\frac{2.16}{4}\times100\\\\\Rightarrow\ P=54\%

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Answer:

A) Maia had 1920 beads more.

B) Maia had 2544 beads at first.

Step-by-step analysis:

Let x denote the beads with Jenny and y for Maia.

The information provided states that Maia possesses 2064 beads more than Jenny, which can be represented mathematically as:

y=x+2064...(1)

Additionally, after Maia made a necklace with 144 beads, she had five times more beads than Jenny.

This can also be formulated as an equation:

y-144=5x...(2)

A) Since Maia had 2064 beads more than Jenny before using 144 beads, we calculate her final bead count by subtracting 144 from 2064.

\text{Number of beads Maia had more than Jenny in the end}=2064-144

\text{Number of beads Maia had more than Jenny in the end}=1920

Thus, Maia is left with 1920 beads more than Jenny.

B) To solve this system of linear equations, we will utilize the substitution method.

By inserting equation (1) into equation (2), we arrive at:

x+2064-144=5x

x+1920=5x

x-x+1920=5x-x

1920=4x

Now, let's divide our equation by 4.

\frac{1920}{4}=\frac{4x}{4}

480=x

Now, we'll substitute x=480 into equation (1) to isolate y.

y=480+2064

y=2544

Conclusively, Maia initially had 2544 beads.

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Question 1: (2.2, -1.4). Question 2: (1.33, 1). Providing a detailed analysis, the equations for the given lines are specified as (1) passing through points (0, 2.5) and (2.2, 1.4), and (2) through (0, -3) and (2.2, -1.4). We are tasked with locating a common solution or intersection of these equations. This leads to finding x = 2.2, and consequently y = -1.4. Therefore, the solution set is (2.2, -1.4). For question 2, the equations yield a solution of (1.33, 1).
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Answer:

A) The total duration needed to paint the room is 50 minutes.

B) To paint 64% of the room takes 32 minutes.

Step-by-step explanation:

Given as:

After 18 minutes, 64% of the room still requires painting.

Therefore, within 18 minutes, (100% - 64% = 36%) of the room has been painted

Let T minutes be the total time required to paint the entire room.

Now, according to the question

A ) Using the unitary method

∵ In total, 36% of the room is covered in 18 minutes

Thus, in total time of \dfrac{18}{36} minutes, 1% of the complete room is painted.Consequently, 100% of the room would be painted in \dfrac{18}{36} × 100 minutes

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Thus, T = 50 min

Therefore, the duration needed to paint the entire room = T = 50 minutes

Thus, the time required to finish painting the entire room is 50 minutes. Answer

B) Again

Time taken to paint 64% of the room = x minutes

∵ 36% of the room has been painted in a total of 18 minutes

Thus, 1% of the entire room gets painted in \dfrac{18}{36} minutes

Consequently, painting 64% of the room will take \dfrac{18}{36} × 64 minutes

i.e x = \dfrac{18\times 64}{36}

Thus, x = 32 min

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Preparation Time: 4:00am

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Detailed Breakdown:

An illustrative depiction of the question has been provided in an image format for clarity.

From the information given, it is noted that her store order arrived on 12/3/2016 at 4am, confirming that both the prep date and time are 12/3/2016 and 4am respectively. The product has a printed expiration date of 1/17/2017, logically indicating that its expiration time is also 4am, in line with the prep time; adding 24 hours leads us back to the same time on the expiration date. Furthermore, we were informed that she utilized the product on 12/7/2016, which marks the initial use date. Based on this information, we can summarize as follows:

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Expiration Time: 4:00am

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Preparation Time: 4:00am

Initial Usage Date: 12/7/2016

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