QR, I want to see what alternate way to solve these problems

[299678]

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Q. what is selling price per kg of a mixture containing 4 kg of a tea A at $34 per kg and 4 kg of a tea B at $16 kg and sold 20% profit?

Q. A vender sells 10 cucumbers for a dollar making a loss of 10%. How many cucumbers did he buy for a dollar?

Q. A donut shop bakes a dozen donuts at a cost of $4. To achieve a 33% profit on sale, what is minimum sale price the donut shop should set for each donut?

Q. The shop keeper unpack his goods to find 6 items missing. He had planned to obtain a profit of 10% by selling the goods, at the marked price, but now he incurs a loss of 5%. How many items did he purchased before they went missing

Q. Sales tax on sugar is reduced by 20%. If the revenue from the sales on sugar remains unaltered by what % must the sales have increased?

 

[299678]

Bump

 

[RSD2014]

Bump

I recognize 1 question. Where are these questions from?

 

[TexasOMFS]

For this question you should first realize that it's a 1:1 ratio of amount of tea A to amount of tea B. Therefore the amount for one kg of a 50/50 mixture of both is simply the average of the price per kg of each. Consequently the retailer has to pay (34+16)/2 or 25 dollars for a kg of this mixture. To sell it at a 20% profit they must sell it at 120% of 25 or $30 dollars.

He sold 10 cucumbers at 90% of the price he originally paid for them. You can set this up as a ratio. 90/100=1/X. X=$1.11. However remember that he paid $1.11 for 10 cucumbers, so that translates to roughly $.11/cucumber. He would've been able to buy 9 cucumbers for a dollar.

Once again, you must figure out what is 33% of the original cost of goods sold and add that to 4. $1.33 would be slightly under 33% of 4 while $1.34 would be slightly above 33% of 4. You want to profit at least 33% so use $1.34, they must sell the donuts for $1.34 + $4 = $5.34

Ignore the information they give you about selling the goods as it is distractor information. We know that he lost 6 items which is equal to 5% of his total inventory of items. Therefore he had purchased 120 items originally.

For this one I would make up some numbers, it's the easiest way to see the relationships. Let's say sugar cost you $100/lb, with a 50% sales tax. In this situation a lb of sugar would cost you $150. If sales tax is lowered by 20% (ie. cost of sales tax goes down from $50 to $30), and you still must get to $150, then the revenue from sugar sold increased from $100 to $120. This corresponds to a 20% increase in sales as well. Some ppl might have been able to tell from just looking at it but it's better to be safe than sorry always.

Sorry I tried quoting your text but I kept getting an error message that said, please lengthen your post to 1 character...it wouldn't let me post.
Hope that helps.

 

[299678]

wow
Your explanation are much better than Crack DAT Math guy. Thank you for your great explanations. I knew the way to solve the problem, but it took me more than 3 minutes to solve it for each question, so I posted it on here. Thank you

 

[299678]

For this question you should first realize that it's a 1:1 ratio of amount of tea A to amount of tea B. Therefore the amount for one kg of a 50/50 mixture of both is simply the average of the price per kg of each. Consequently the retailer has to pay (34+16)/2 or 25 dollars for a kg of this mixture. To sell it at a 20% profit they must sell it at 120% of 25 or $30 dollars.

He sold 10 cucumbers at 90% of the price he originally paid for them. You can set this up as a ratio. 90/100=1/X. X=$1.11. However remember that he paid $1.11 for 10 cucumbers, so that translates to roughly $.11/cucumber. He would've been able to buy 9 cucumbers for a dollar.

Once again, you must figure out what is 33% of the original cost of goods sold and add that to 4. $1.33 would be slightly under 33% of 4 while $1.34 would be slightly above 33% of 4. You want to profit at least 33% so use $1.34, they must sell the donuts for $1.34 + $4 = $5.34

Ignore the information they give you about selling the goods as it is distractor information. We know that he lost 6 items which is equal to 5% of his total inventory of items. Therefore he had purchased 120 items originally.

I agree with your answer, but >>> correct answer is 44

For this one I would make up some numbers, it's the easiest way to see the relationships. Let's say sugar cost you $100/lb, with a 50% sales tax. In this situation a lb of sugar would cost you $150. If sales tax is lowered by 20% (ie. cost of sales tax goes down from $50 to $30), and you still must get to $150, then the revenue from sugar sold increased from $100 to $120. This corresponds to a 20% increase in sales as well. Some ppl might have been able to tell from just looking at it but it's better to be safe than sorry always.

>>>> correct answer is 25%

Sorry I tried quoting your text but I kept getting an error message that said, please lengthen your post to 1 character...it wouldn't let me post.
Hope that helps.

I found two of answers were incorrect, could you be able to fix it for me?

 

[299678]

Q. what is selling price per kg of a mixture containing 4 kg of a tea A at $34 per kg and 4 kg of a tea B at $16 kg and sold 20% profit?

Q. A vender sells 10 cucumbers for a dollar making a loss of 10%. How many cucumbers did he buy for a dollar?

Q. A donut shop bakes a dozen donuts at a cost of $4. To achieve a 33% profit on sale, what is minimum sale price the donut shop should set for each donut?

Q. The shop keeper unpack his goods to find 6 items missing. He had planned to obtain a profit of 10% by selling the goods, at the marked price, but now he incurs a loss of 5%. How many items did he purchased before they went missing

Q. Sales tax on sugar is reduced by 20%. If the revenue from the sales on sugar remains unaltered by what % must the sales have increased?

This is the way CDM solve for problem #4
total price = Y, total # of items = Y
1.1Y(x-6) = 0.95*x*Y, solve for X = 44
I don't understand why we put (x-6) on left side
What I did was
1.1Y*x = 0.95*(x-6)*Y

 

[Streetwolf]

This is the way CDM solve for problem #4
total price = Y, total # of items = Y
1.1Y(x-6) = 0.95*x*Y, solve for X = 44
I don't understand why we put (x-6) on left side
What I did was
1.1Y*x = 0.95*(x-6)*Y

Not sure what that's all about but filling in x = 44 only works for their equation.

What I would do is look at the problem and note that the difference between 110% and 95% (or 15%) comes from 6 items. So those 6 items make up 15% of the cost. Each item therefore makes up 2.5%. Since he wanted to have 110%, he had 44 items originally.

 

[UCB05]

I'm guessing the other incorrect answer is this:

Once again, you must figure out what is 33% of the original cost of goods sold and add that to 4. $1.33 would be slightly under 33% of 4 while $1.34 would be slightly above 33% of 4. You want to profit at least 33% so use $1.34, they must sell the donuts for $1.34 + $4 = $5.34

$5.34 would be the proper price per dozen. Just divide by 12 to get the price per donut

 

[sfoksn]

How would you do the last problem?

I tried plugging in numbers, and I get 15%.

(100 crops)(10 dollars per crop)(1.5) = 1500 from 100 crops, 10 dollars each, with 50% tax.

(x crops)(10 dollars per crop)(1.3) also must equal 1500, and if you solve for x it comes out to be 115ish..

 

[299678]

Sales tax = Y, reduced sales Tax = 0.8Y
Sales increasement = x
0.8Y*x = Y, x = 1.25, so 25% increasement of sales

 

[TexasOMFS]

Not sure what that's all about but filling in x = 44 only works for their equation.

What I would do is look at the problem and note that the difference between 110% and 95% (or 15%) comes from 6 items. So those 6 items make up 15% of the cost. Each item therefore makes up 2.5%. Since he wanted to have 110%, he had 44 items originally.

Ah, yes that makes sense. Could u walk me through the logic of that? I'm not sure why, but even when I re-read the question I interpret it as him losing 6 units which is 5% of his total inventory. Is the question badly worded or is it me?

 

[TexasOMFS]

^Hmm nvm, I valued his original inventory at his expense of purchasing the merchandise (100%) not at the unearned revenue he was hoping to obtain from it (110%). Still, it's like how do you really lose the revenue (that additional 10%) when you don't even know whether stock will move. In my opinion, it's a poorly worded question. At least, it clashes with what I've been learning in my business classes haha.

 

[TexasOMFS]

Oh and sorry for the triple post but I just realized what I messed up with on the last question. Using my previous example, we have to account for the change in revenue earned from sugar sales BEFORE we calculate the tax %, because the tax % depends on the new revenue. The fallacy with my solution was that I simply decreased the tax amount by 20% assuming still $100 in sales, then I increased the sales to meet the $150 total, sorry idk why I did that. You can derive an equation to solve this probably but I'm too lazy to so I'd just say kind of play with the numbers until you realize that if the tax decreases from 50 to 25 (by 25) with a corresponding increase of revenue from 100 to 125, 25 is 20% of 125 (the new revenue) so taxes did indeed decrease by 20% and sales increased by 25 also, which is 25% of 100 (the original revenue). That problem is a lot tougher than it initially looked, it definitely had me fooled.