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Recent problems solved by 'stanbon!'
stanbon! answered: 97 problems
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Word_Problems_With_Coins/11267: John has 7 more pennies than nickels and 2 fewer quarters than pennies. His total amount of money is $2.87. How many of each type of coin does he have?
1 solutions
Answer 11624 by stanbon!(97)   on 2005-12-24 12:27:22 (Show Source):
You can put this solution on YOUR website!Let number of nickels be "x".
Then number of pennies is "x+7"
And number of quarters is "x+7-2" = "x+5"
Value of nickels is (5)x cents
Value of pennies is (1)(x+7)= x+7 cents
Value of quarters is (25)(x+5)= 25x+125 cents
EQUATION:
Value of nickels + Value of pennies + Value of quarters = 287 cents
5x + x+7 + 25x+125 = 287
31x = 155
x = 5 (number of nickels)
x+7 = 12 (number of pennies)
x+5 = 10 (number of quarters)
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Equations/23140: I am having problems with solving equations. The following are equations and it's methods that I don't seem to understand. Thank you for your assistance!
Solve using the addition (elimination) method.
2x + 3y = -16
5x-10y=30
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Solve using the addition (elimination) method
2y - 8 = -2x - 8x
8x - 3y = 31 + y
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Solve using the substitution method
x = 3y + 7
x = 2y - 1
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Solve using the substitution method
4x + 3y = 0
2x - y = 0
1 solutions
Answer 11620 by stanbon!(97) on 2005-12-24 08:59:08 (Show Source):
You can put this solution on YOUR website!Elimination:
1st: 2x+3y=-16
2nd: 5x-10y=30
Multiply 1st by 5 and 2nd by 2 to get the following:
1st: 10x+15y=-80
2nd: 10x-20y=60
Now subtract the 2nd from the 1st to eliminate the x's:
35y = -140
y = -4
Substitute that value of "y" into the original 1st
equation to solve for "x":
2x+3(-4)= -16
2x-12 = -16
x = -2
Check this answer of x=-2 and y=-4 in the 2nd original equation:
5(-2)-10(-4)= 30
-10+40 = 30
30 = 30
Cheers,
Stan H.
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Word_Problems_With_Coins/12023: A collection of 30 coins worth $5.50 consists of nickles, dimes, and quarters. There are twice as many dimes as nickles. How many quarters are there?
1 solutions
Answer 11619 by stanbon!(97) on 2005-12-24 08:46:31 (Show Source):
You can put this solution on YOUR website!Let number of nickels be "x".
Then number of dimes is "2x".
And number of quarters is "30-3x"
Value of nickels is (5)x cents
Value dimes is (10)2x = 20x cents
Value of quarters is (25)(30-3x)= 750-75x cents
EQUATION:
Value of nickels + Value of dimes + Value of quarters = 550 cents
5x + 20x + 750-75x = 550
-50 x = -200
x = 4 (number of nickels)
2x = 8 (number of dimes)
30-3x = 30-12 = 18 (number of quarters)
Cheers,
Stan H.
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Graphs/22433: (2,1); m=1 Write an equation in standard form. Please help
1 solutions
Answer 11610 by stanbon!(97) on 2005-12-23 20:54:03 (Show Source):
You can put this solution on YOUR website!y=mx+b
The point (2,1) gives you an "x" and a "y" value
and you are also given the "m" value. Substitute
to get 1 = (1)(2)=b
1 = 2b
b = 1/2
The equation is y = x+1/2
Now, put that in standard form which is ax + by = c
Multiply (y=x+1/2) thru by "2" to get:
2y= 2x + 1
Write this as
2x+(-2y)= -1
That is the equation in standard form.
Cheers,
Stan H.
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Expressions-with-variables/22550: how do u write an algebraic expression to represent the cost of a concert ticket,h, with a service of $6.75
1 solutions
Answer 11609 by stanbon!(97) on 2005-12-23 20:43:48 (Show Source):
You can put this solution on YOUR website!If you buy one ticket cost = $6.75 + h
If you buy two tickets cost = $6.75 +2h
If you buy three tickets cost= $6.75 + 3h
Let "x" be the number of tickets you are going to buy.
Then Cost = $6.75 + xh
Cheers,
Stan H.
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Equations/23138: I am completely lost in trying to solve the following equations. I respectfully ask for your help and assistance. Thank you.
Robert
1.
Use the addition method to solve the following system of equations:
(1/3)X + Y = 3 AND (1/2)X - (1/4)Y = 1
2.
Use the substitution method to solve the following system of equations:
2x+5y = 1 and -x+6y = 8
1 solutions
Answer 11608 by stanbon!(97) on 2005-12-23 20:37:37 (Show Source):
You can put this solution on YOUR website!Prob. #1
First, get rid of the fractions:
Multiply 1st equation thru by 3 to get:
X + 3Y=9
Multiply 2nd equation thru by 4 to get:
2x- Y = 4
Now multiply this last equation thru by 3 so we can get rid of the Y's.
6X -3Y = 12
This is now the equations you are working with:
1st: X +3Y= 9
2nd: 6X-3Y= 12
Now add the two equations to get:
7x = 21
x = 3
Put this value into one of the early equations to solve for "Y".
3 + 3Y = 9
3Y = 6
Y = 2
Solution: X= 3 and Y= 2
Check that answer in the original equations.
2nd Problem:
2x+5y=1
x=6y-8
Substitute this value of "x" into the 1st equation to get:
2(6y-8)+5y = 1
12y-16+5y = 1
17y = 17
y = 1
Substitute that value into one of the original equations to get:
x=(6(1))-8
x= 6-8=2
Solution:
x = 2 and y = 1
Check that answer in the othe original equation.
Cheers,
Stan H.
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Travel_Word_Problems/23139: a boat takes 2 hours longer to go 45 miles up a river than to return. If the boat's speed in still water is 12 mph, what is the rate of the current.
Can you please show you step this time.
1 solutions
Answer 11607 by stanbon!(97) on 2005-12-23 20:10:47 (Show Source):
You can put this solution on YOUR website!Downstream Data: distance= 45; rate=12+c; time=45/(12+c)
Upstream Data: distance = 45: rate = 12-c; time= 45/(12-c)
EQUATION:
Time Upstream - Time Downstream = 2 hours
45/(12-c) - 45/(12+c) = 2
Divide thru by 45 to get:
1/(12-c) - 1/(12-c) =2/45
Simplify :
45[(12+c)-(12-c)]= 2[(12-c)(12+c)]
45[2c] =2[144-c^2]
90c = 288-2c^2
c^2+45c-144=0
(c-3)(c+48)=0
current speed = 3 mph
Cheers,
Stan H.
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Travel_Word_Problems/23133: The exam starts at school at 09:00. You want to get there 15min early. it takes 20 min to 30 min to get to school, depending on the buses. You plan to study for 1 hour at home. It will take you 1 hour to shower, dress, and eat breakfast. For what time should you set your alarm?
1 solutions
Answer 11586 by stanbon!(97) on 2005-12-23 10:52:18 (Show Source):
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Linear-systems/23134: Sir, pl. help to solve this simple interest question.
A man borrowed Rs. 80,000 from a bank at rate 7% per annum. After 2 years, he returned Rs. 30,000. How much balance amount he has to pay at the end of 5th year. Ans is Rs. 71700.
1 solutions
Answer 11585 by stanbon!(97) on 2005-12-23 10:48:58 (Show Source):
You can put this solution on YOUR website!Is this what you mean?
He accumulated simple (not compound) interest on the loan
for two years at 7% annual rate, then he paid off
30000 of the combined pricipal and accumulated interest.
Then he accumulated 7% simple (not compound) interest for
three years on that remaining balance and finally paid
off the entire accumulated balance?
If your answer to this question is , yes, I do not see
how the answer to the question is 71700.
Cheers,
Stan H.
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Linear-equations/23081: write an equation of the line that passes through the given two points.
(-7,8)(-4,11)
(7,0)(27,-60)
(2,3)(8,0)
1 solutions
Answer 11576 by stanbon!(97) on 2005-12-22 21:34:53 (Show Source):
You can put this solution on YOUR website!Let's try the 1st pair of points. The others are worked in the same way.
The two-point form is y-y1 = m (x-x1)
where m= (change in y)/(change in x)
So for your problem m = (11-8)/(-4-(-7)) = 3/3=1
Now the x1,y1 comes from one of your two points; it doesn't
matter which point you pick out. We'll try (-4,11).
Then y-(11) = (1)(x-(-4)
And y-11 = (x+4)
Then y = x+4+11
y = x+15
Cheers,
Stan H.
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Word_Problems_With_Coins/12187: A change purse contains 14 coins consisting of nickels and dimes and having a total value of $1.10. How many nickels are there?
1 solutions
Answer 11573 by stanbon!(97) on 2005-12-22 21:05:46 (Show Source):
You can put this solution on YOUR website!Let number of nickels be "x".
Then number of dimes is "14-x"
Value of nickels is (5)x cents
Value of dimes is (10)(14-x) = (140-10x) cents
EQUATION:
Value of nickels + Value of dimes is 110 cents.
5x +140-10x = 110
-5x = -30
x = 6 ( number of nickels)
Cheers,
stan H.
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Word_Problems_With_Coins/12236: coin collection worth $2.90 contains nickels, dimes, and quaters. There are three times as many dimes as there are nickels, and the number of quarters is 2 more than the number of nickels
1 solutions
Answer 11572 by stanbon!(97) on 2005-12-22 20:47:20 (Show Source):
You can put this solution on YOUR website!Let number of nickels be "x".
Then number of dimes is "3x".
And number of quarters is "x+2".
Value of nickels is (5)x cents.
Value of dimes is (10)(3x)= 30x cents
Value of quarters is (25)(x+2)=25x+50 cents
EQUATION:
Value of nickels + Value of dimes + Value of quarters is 290 cents.
5x + 30x + 25x+50 = 290
60x=240
x= 4 (number os nickels)
3x= 12 (number of dimes)
x+2= 6 (number of quarters)
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Graphs/23129: x>7/8y +5
2x>=3/4y+7
Determine if the given points are solutions to the given systems of inequalities.
a. The point is a solution to the system
b. The point is not a solution to the system.
1 solutions
Answer 11569 by stanbon!(97) on 2005-12-22 15:43:48 (Show Source):
You can put this solution on YOUR website!You need to post the points along with the set of inequalities.
If you want to do the problem yourself. take one of the point
values (the x value and the y value) and substitute them into
both of your inequalities. If the numerical result is "true"
the point is in the solution of the system. If the numerical
result is "false" the point is not.
Cheers,
Stan H.
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Quadratic_Equations/23132: Please help me, I need a breif explanation of how the quadratic equation works, because I need to explain it in a problem, but I got the answer to it on my graphing calculator, and I never used it before in school. All I know about it is that is serves as a rule for the problem. Help!
1 solutions
Answer 11568 by stanbon!(97) on 2005-12-22 15:38:18 (Show Source):
You can put this solution on YOUR website!I suggest you use Google to search for "Math World Quadratic Equation".
There the quadratic formula is derived and it's use is explained.
Cheers,
Stan H.
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Word_Problems_With_Coins/23107: This is a question I REALLY don't understand I hope you might be able to help me.
"Carey has $2.55 made up of pennies, dimes and quarters. She has as many dimes as pennies and she ahs eighteen coins in all. How many quarters does she have?"
Well I tried this way but It didn't work and I'll show you
Let x = pennies 0.01x
x = dimes 0.1x
18 - x = 0.25 (18 - x)
And I wrote as this way
0.01x + 0.1x + 0.25(18 - x) = $2.55
You think you can tell me what I did wrong?
1 solutions
Answer 11539 by stanbon!(97) on 2005-12-21 22:28:19 (Show Source):
You can put this solution on YOUR website!You did fine till you got to the equation.
You have x pennies and x dimes so you must have (18-2x) quarters.
Make that change and I think everything will turn out right.
Cheers,
stan H.
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Geometry_Word_Problems/23073: A tree (altitude =a) breaks somewhere in its height and falls over.
The tip of the tree touches ground at 20' from stump (base b= 20')
The created hypotonuse (c) is equal to 2 times a.
What was the height of the tree before the tree broke and fell?
given that: a^2 + b^2 = c^2
I end up with x^2 + 20^2 = 2x^2
Now where do I go to finish? (Next: x^2 - 2x^2 = 400)?
I can't remember how to solve this. My book has no literal explanation of the steps (I'm too dumb to derive the solution)
1 solutions
Answer 11524 by stanbon!(97) on 2005-12-21 17:29:53 (Show Source):
You can put this solution on YOUR website!How can a tree that is "a" high have a fallen part
that is "2a" in length?
Please check the statement of your problem.
Cheers,
Stan H.
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Coordinate-system/22669: C(-5, -2); slope = 1/4
1 solutions
Answer 11520 by stanbon!(97) on 2005-12-21 17:06:49 (Show Source):
You can put this solution on YOUR website!The line has the form y=mx+b where "m" is the slope.
Substitute m=1/4; x=-5; y=-2 to get the following:
-2=(1/4)(-5)+b
-2=(-5/4)+b
Add 5/4 to both sides to get the following:
b=-3/4
So the equation is y=(1/4)x+(-3/4)
Cheers,
Stan H.
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real-numbers/23089: Can you help me break down the following equation? I have most of it but I am having a problem getting the fractions back into decimals once I have converted and solved the problem.
thank you, Melonie
-3/5[2/3 - 1/2(3/4-1/2)]
1 solutions
Answer 11519 by stanbon!(97) on 2005-12-21 16:48:45 (Show Source):
You can put this solution on YOUR website!Work with the parenthesis firs:
3/4-1/2= 3/4-2/4 = 1/4
Multiply this by (1/2) to get 1/8
Then 2/3-1/8 = (16-3)/24 = 13/24
Multiply by -3/5 to get -39/120
Cheers,
Stan H.
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Signed-numbers/23091: 3 2
4 - - 2 -
5 3
1 solutions
Answer 11518 by stanbon!(97) on 2005-12-21 16:21:18 (Show Source):
You can put this solution on YOUR website!Convert the 4 3/5 to 5ths. "4" is 20/5. Add 3/5 to get 23/5
Convert the 2 2/3 to 3rds. "2" is 6/3. Add 2/3 to get 8/3
The problem is now the following:
23/5 - 8/3
Since the denominators are not the same determine the LCD of 5(3)= 15
Now convert each fraction to 15ths.
(3/3)(23/5) = 69/15
(5/5)(8/3) = 40/15
The problem is now the following:
69/15 - 40/15 = 29/15
Cheers,
Stan H.
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Geometric_formulas/22876: Find the solution set for 15X^2+19X+6=0
Thanks in advance
1 solutions
Answer 11515 by stanbon!(97) on 2005-12-21 14:57:56 (Show Source):
You can put this solution on YOUR website!Use what is called the "AC Method" to factor this trinomial
In your problem a=15, b=19, c=6
Form the product ac= 90
Notice that b= 19
Now find two numbers whose product is 90 and whose sum is 19.
They are 9 and 10.
Rewrite your problem, substituting 9x + 10x in place of 19x
to get the following:
15x^2 +9x +10x +6
Now factor the 1st two terms and then the last two terms as follows:
3x(5x+3)2(5x+3)
= (5x+3)(3x+2
By the way. If there are not two numbers whose product is AC and
whose sum is B you will have to use the binomial formula to find
the factors.
Cheers,
Stan H.
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Rational-functions/21279: perform the indicated operation, simplify the answer, show work please
x/x-3 + 2/3x+4
i had trouble finding the LCD, please help and solve, thank you
1 solutions
Answer 11512 by stanbon!(97) on 2005-12-21 14:36:05 (Show Source):
You can put this solution on YOUR website!The LCD is (x-3)(3x+4)
Multiply num. and denom. of 1st fraction by (3x+4) to get the following:
x(3x+4)/LCD
Multiply num. and denom. of the 2nd fraction by (x-3) to get the following:
2(x-3)/LCD
Both denominators are now the same so combine the numerators to get the following:
[3x^2+4x +2x-6]/LCD = [3x^2+6x-6]/LCD = 3[x^2+2x-2]/LCD
The numerator is not "neatly" factorable now leave it alone.
Cheers,
Stan H.
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Mixture_Word_Problems/23078: Two Trains leave Chicago, one traveling east at 30 miles per hour and one traveling west at 40 miles per hour. When will the trains be 280 miles apart?
1 solutions
Answer 11511 by stanbon!(97) on 2005-12-21 14:20:50 (Show Source):
You can put this solution on YOUR website!Draw the picture.
East train data: distance = x; rate=30; time = x/30
West train data: distance = 280-x; rate = 40; time = (280-x)/40
EQUATION:
Time East = Time West
x/30 = (280-x)/40
40x = 30(280-x)
40x = 30(280)-30x
70x =30(280
x = 3(40)
x = 120 mph
Therefore time = x/30 = 120/30= 4 hours
Cheers,
Stan H.
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