more math problems. need help

[BodybldgDoc]

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If anyone could please explain on how to work these out, i'd appreciate it.


1.A fly sits at the edge of a 12 inch diameter phonograph record that is playing at 331/3 revolutions per minute. Approximately how fast, in feet per minute, is the fly moving?
A 3
B 33
C 50
D 100
E 396

Answer= D How do you convert revolutions to feet?

2. Sales reductions force a factory to cut back its output by 20%. By what percentage must the reduced sales be increased to allow production to be brought back to normal?
A 40
B 30
C 35
D 20
E 25

Answer= E <-- i dont get the logic behind this one. i figured the answer would be D

3. The current sales price of a power drill is $117.00 This is $30.00 more than half the list price. At what discount is the drill being sold?
A 32.8%
B 25.6%
C 74.4%
D 67.2%
E 48.7%


Answer= A. please help i have no idea on this one.

 

[Mila]

2. Sales reductions force a factory to cut back its output by 20%. By what percentage must the reduced sales be increased to allow production to be brought back to normal?
A 40
B 30
C 35
D 20
E 25

Answer= E <-- i dont get the logic behind this one. i figured the answer would be D

Lets say that the initial output of the factory is initial output = 100.
When we cut back output by 20%, we have reduced output = 80.
Now we need to increase this reduced output (which is 80) by a certain percentage to bring it back to initial output (100).

20% of 80 is only 16, [not to be confused with 20% of 100] so if we increase reduced output (80) by 20%, we will have final output = 96 which is too low.
However, 25% of 80 is 20. So if we increase the reduced output (80) by 25%, then we have initial output (100) again.
So the answer choice is E - 25%.
I hope that made sense... sorry if it's confusing at all.

 

[Streetwolf]

If anyone could please explain on how to work these out, i'd appreciate it.


1.A fly sits at the edge of a 12 inch diameter phonograph record that is playing at 331/3 revolutions per minute. Approximately how fast, in feet per minute, is the fly moving?
A 3
B 33
C 50
D 100
E 396

Answer= D How do you convert revolutions to feet?

2. Sales reductions force a factory to cut back its output by 20%. By what percentage must the reduced sales be increased to allow production to be brought back to normal?
A 40
B 30
C 35
D 20
E 25

Answer= E <-- i dont get the logic behind this one. i figured the answer would be D

3. The current sales price of a power drill is $117.00 This is $30.00 more than half the list price. At what discount is the drill being sold?
A 32.8%
B 25.6%
C 74.4%
D 67.2%
E 48.7%


Answer= A. please help i have no idea on this one.

1. He's 1/2 foot from the middle so the diameter is 1 foot. The circumference is (pi) feet. So there are (pi) feet per revolution (that's where revolutions come from in the problem). Multiply this by 33 1/3 (or 100/3). So you do pi * 100/3. It pains me to say this as a math major, but round pi to about 3. Then 3 * 100/3 = 100. None of the other answers come this close so it must be right.

2. Cut back by 20% means there is still 80% of the output there. So let x be the amount of output. The new amount is 0.8x. You want to multiply it by something to get it back to just x. So let that something be 'n' (n will be your answer). So n * 0.8x = x. So n = 1/0.8 = 1.25 which means your answer is 125% of the new amount. But it wants the percent INCREASE. So 125% - 100% = 25%, your answer.

3. '$117.00 is $30.00 more...' it is $30.00 more than $87.00 which is 'half the list price' means the list price is 2 * $87.00 = $174.00. The discount is $174.00 - $117.00 = $57.00. The discount is $57.00 / $174.00 which is close to 33%. The answer is A.

 

[Mila]

3. The current sales price of a power drill is $117.00 This is $30.00 more than half the list price. At what discount is the drill being sold?
A 32.8%
B 25.6%
C 74.4%
D 67.2%
E 48.7%


Answer= A. please help i have no idea on this one.

OK...
The current sales price ($117) is $30 more than half the list price, therefore:
Half the list price = $117 - $30 = $87
That means that original list price = $87 X 2 = $174.

We need to figure out what percentage is taken off of $174 to give us the sale price of $117.

Two ways to think of this:
(1) We know that this sales price is $57 cheaper that the list price ($174 - $117).
So we need to find out what percentage $57 is of $174:

57/174 --> this is similar to 60/180 which is a third or 33%. So approximately one third has been taken off the list price and the sales price is 2/3 that of the list price.
The drill is being sold at a 32% discount.

(2) the second way to see this is just 117/174 (which is similar to 120/180)
if you can see that this will be roughly 2/3 from the numbers then you know that the discount is 1/3 giving you the closest answer to 33%

 

[BodybldgDoc]

thanks mila your explanations were great and thanks to street wolf as well.