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oberobic answered: 2303 problems
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1 solutions
Answer 342156 by oberobic(2304)   on 2011-10-07 23:11:42 (Show Source):
You can put this solution on YOUR website!y=3x+1.
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substitute for y
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3(3x+1) -7x = 9
9x +3 -7x = 9
2x = 6
x = 3
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substitute for x
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y =3(3) +1
y = 10
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check using 3y-7x = 9
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3y -7x = ??
3(10) -7(3) = 30 -21 = 9
correct
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Answer: x=3, y=10
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Done.
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test/511344: Kristen can finish a task in 5 hours. When Cristina helps Kristen, they can finish the task in 4 hours. How long does it take Cristina to finish the task if she works alone?
1 solutions
Answer 342155 by oberobic(2304) on 2011-10-07 23:07:31 (Show Source):
You can put this solution on YOUR website!Kristen does 1/5 of the whole job per hour.
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Cristina does the the job at an unknown rate per hr: 1/C
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Working together they can do the whole job in 4 hrs.
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(1/5 + 1/C)*4 = 1 whole job
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1/5 + 1/C = 1/4
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1/C = 1/4 - 1/5
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1/C = 5/20 - 4/20
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1/C = 1/20
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Cristina can do the job working alone in 20 hr.
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Check to see if they can do the job in 4 hr working together.
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(1/5 + 1/20)* 4 = ??
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(4/20 + 1/20) *4 = 5/20 * 4 = 1/4*4 = 1
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Correct.
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Answer: Cristina takes 20 hr working alone.
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Done.
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test/511295: Kristen can finish a task in 5 hours. When Cristina helps Kristen, they can finish the task in 4 hours. How long does it take Cristina to finish the task if she works alone?
1 solutions
Answer 342154 by oberobic(2304) on 2011-10-07 23:05:39 (Show Source):
You can put this solution on YOUR website!Kristen does 1/5 of the whole job per hour.
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Cristina does the the job at an unknown rate per hr: 1/C
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Working together they can do the whole job in 4 hrs.
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(1/5 + 1/C)*4 = 1 whole job
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1/5 + 1/C = 1/4
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1/C = 1/4 - 1/5
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1/C = 5/20 - 4/20
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1/C = 1/20
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Cristina can do the job working alone in 20 hr.
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Check to see if they can do the job in 4 hr working together.
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(1/5 + 1/20)* 4 = ??
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(4/20 + 1/20) *4 = 5/20 * 4 = 1/4*4 = 1
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Correct.
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Answer: Cristina takes 20 hr working alone.
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Done.
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Equations/511325: Solve the system of equations using elimination. x+y= -8, -x+4y= 13
1 solutions
Answer 342150 by oberobic(2304) on 2011-10-07 22:55:52 (Show Source):
You can put this solution on YOUR website!x +y = -8
-x + 4y =13
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multiply the first equation by 4 and then subtract
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4x +4y = -32
-x +4y = 13
--------------
5x +0y = -45
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x = -9
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-(-9) + 4y = 13
9 + 4y = 13
4y = 4
y = 1
.
check
x + y = ??
-9 +1 = -8
correct
.
check
-x +4y = ??
-(-9) +4(1) = 9+4 = 13
correct
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Answer: x=-9, y=1
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Done.
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Equations/511326: Use the elimination method to solve the system of equations. 5u+3v= -16, 2u+v= -7
1 solutions
Answer 342140 by oberobic(2304) on 2011-10-07 22:27:08 (Show Source):
You can put this solution on YOUR website!5u+3v= -16
2u+v= -7
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multiply the second equation by 3 and then subtract
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5u +3v = -16
6u +3v = -21
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-u +0v = 5
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u = -5
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5(-5) + 3v = -16
-25 + 3v = -16
3v = 9
v = 3
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check using the second equation
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6u + 3v = ??
6(-5) + 3(3) = -30 +9 = -21
correct
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Answer u = -5, v = 3
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Done.
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Age_Word_Problems/510962: The father is 35 the son is 9. How many years will it take the son to be 3 times his fathers age. I have two different answers that I do not know if they are correct. I have tried 35-9= 26X3 = 78. I have also tried 35x3= 105/9 =11.667.
1 solutions
Answer 341952 by oberobic(2304) on 2011-10-06 22:31:14 (Show Source):
You can put this solution on YOUR website!35+x = 3(9+x)
35+x = 27 + 3x
-2x = -8
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x = 4
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In 4 years, the father will be 39 and the son will be 13. 39 = 3*13.
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It is impossible for a son to be 3 times the father's age ever, so I solved it the other way.
The father will be 3 times the son's age in 4 years.
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Done.
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Graphs/510958: What is the intercepts?
Find the x and y intercepts of 3x-5y=15; then use the intercepts to the graph the line.
1 solutions
Answer 341949 by oberobic(2304) on 2011-10-06 22:26:04 (Show Source):
You can put this solution on YOUR website!3x -5y = 15
-5y = -3x + 15
y = -3/-5x + 15/-5
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y = 3/5x -3
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y-intercept occurs where x=0: (0,-3)
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x-intercept occurs where y=0: (5,0)
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Age_Word_Problems/510937: Matthew is 3 times as old as Jenny. In 7 years he will be twice as old as she will be then. How old is each now.
I have figured out the answer, but not how to work the problem. I tried:
x + 1/3X = 2 times X + 7 + 1/3 X + 7 which is completely wrong. I have not done a problen where I didn't have a specific number for an answer. Reid
1 solutions
Answer 341941 by oberobic(2304) on 2011-10-06 22:06:18 (Show Source):
You can put this solution on YOUR website!M = 3*J
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In 7 years, their ages will be:
M+7
J+7
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M+7 = 2*(J+7)
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Substitute M=3*J
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3J + 7 = 2J + 14
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J = 7
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M = 3J = 21
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Check their age relationship in 7 years.
M+7 = 28
J+7= 14
M+7 = 2(J+7)
Correct.
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Answer: Matthew is 21, and Jenny is 7.
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Done.
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Money_Word_Problems/510938: Earl worked 20 hours last week. If he earned .50 an hour more but only worked 18 hours, he would have earned the same amount. How much per hour does earl earn?
1 solutions
Answer 341935 by oberobic(2304) on 2011-10-06 22:00:23 (Show Source):
You can put this solution on YOUR website!x = his rate of pay
20x = how much he was paid for working 20 hr
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18*(x+1/2) = 20x
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18x + 9 = 20x
9 = 2x
x = 4 1/2
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20 * 4 1/2 = $90
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18 * 5 = $90
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So the correct answer is $4.50.
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Done.
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Linear-equations/510930: find the equation of the lin in slope intercept form and standard form: contains (5,1) and is perpendicular to y=3
1 solutions
Answer 341933 by oberobic(2304) on 2011-10-06 21:57:28 (Show Source):
You can put this solution on YOUR website!This is a trick question.
The line y=3 means that for all x, from -infinity to +infinity, will have y=3.
There is no change in y, so the slope = 0.
y = 3 can be shown as y = 0x + 3.
The line y=3 is a horizontal line.
.
So, the line perpendicular to it will be a vertical line.
Of course, a vertical line's slope is undefined because there is no change in x for all values or 'y'.
Dividing by 0 is undefined so the slope is undefined, not 0.
To define a vertical line that goes through the point (5,1), simply state x=5.
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Done.
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Equations/510342: Please help me with these three equations.
x = y + 2
1/2x + y = o
y = 4/7x + 3
I am suppose to tell whether y varies directly as x.
Please help I don't understand.
1 solutions
Answer 341796 by oberobic(2304) on 2011-10-05 22:08:07 (Show Source):
You can put this solution on YOUR website!EQ1.
x = y +2
y = x -2
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as x increases, y increases
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EQ2.
1/2x + y = 0
y = -1/2x
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as x increases, y decreases
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EQ3.
y = 4/7x + 3
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as x increases, y increases
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Consider the graphs: EQ1 is red, EQ2 is green & EQ3 is blue.
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Complex_Numbers/510318: sketch the graph y=x(x-3)(x^2-1) finding additional points to sketch on the graph.
I did: (x^2-3x)(x^2-1) = x^4-4x^2+3x
i factored out difference of perfect squares with x^4-4x^2 and got
x(x+2)(x-2) +3x = 0 (to get the x intercepts)
i got my y-int to be (0,0) and my x's to be x=+/-2 and x=0.
so idk if any of that is correct?
1 solutions
Answer 341791 by oberobic(2304) on 2011-10-05 21:38:25 (Show Source):
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Mixture_Word_Problems/510304: chemical is 60% acid and chemical B is 36% acid. How much of each should be mixed together to get 120oz of a chemical that is 52% acid?
1 solutions
Answer 341787 by oberobic(2304) on 2011-10-05 21:27:53 (Show Source):
You can put this solution on YOUR website!With mixture problems, you need to keep track of how much 'pure' stuff you have or need.
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120 oz. of a 52% solution means you need to have .52*120 = 62.4 oz of 'pure' acid in the 120 oz.
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You will combine an unknown amount of one solution, 'x' with another amount to have 120 oz.
So we can use x' and '120-x' as the two volumes.
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The combined solutions are defined by the following equation.
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60%*x + 36%(120-x) = 52%*120
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Solve it.
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.60x + .36(120-x) = .52*120
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multiply by 100 to eliminate decimals
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60x + 36(120-x) = 52*120
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60x +4320 -36x = 6240
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24x = 6240 -4320
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24x = 1920
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x = 80 oz
120-x = 40 oz
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Answer: Combine 80 oz. of 60% solution and 40 oz. of 36% solution.
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Check to be sure the answer is right.
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60%(80 oz) = 48 oz of 'pure' acid
36%(40 oz) = 14.4 oz of 'pure' acid
48 + 14.4 = 62.4 oz. of 'pure' acid in the 120 oz., which is what we need to achieve 52%
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Done.
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Problems-with-consecutive-odd-even-integers/510293: What are all the possible sets of three consecutive odd whole numbers whose sum is less then 45?
1 solutions
Answer 341773 by oberobic(2304) on 2011-10-05 20:55:46 (Show Source):
You can put this solution on YOUR website!Three consecutive odd whole numbers are x, y, and z.
But with three unknowns, we need three equations.
All we have is 1 equation, so we need to define the numbers differently.
x
x+2
x+4
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x +x+2 +x+4 = 45
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3x +6 = 45
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3x = 39
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x = 13
x+2 = 15
x+4 = 17
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13+15+17=45
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Answer: The three consecutive whole odd numbers that total 45 are 13, 15, and 17.
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Done.
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Linear-equations/510275: 5x-2y=4
x+2 y=8
1 solutions
Answer 341771 by oberobic(2304) on 2011-10-05 20:51:21 (Show Source):
You can put this solution on YOUR website!Add the two equations:
| | 5x | -2y | = | 4 |
| + | 1x | +2y | = | 8 |
| | 6x | +0y | = | 12 |
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6x =12
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Solve for 'x'
x = 2
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substitute x=2 to find y
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5(2) -2y = 4
-2y = -6
y = 3
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check this answer using the other equation
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x + 2y = 8 ??
2 + 2(3) = 8
correct.
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Answer: x =2 and y = 3
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Done.
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Circles/510188: Find the circumference and area of a circle with diameter of 18 inches. Use 3.14 for pi. Write your answer as decimals rounded to the nearest hundredth.
1 solutions
Answer 341743 by oberobic(2304) on 2011-10-05 18:49:13 (Show Source):
You can put this solution on YOUR website!circumference = pi*d
d = 18 in.
so
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circumference = pi*18 in.
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pi = 3.14
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circumference = 3.14 * 18 in.
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circumference = 56.52
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Linear-equations/510173: when you graph your lines on the graph how do you find the slope and y intercept?
1 solutions
Answer 341742 by oberobic(2304) on 2011-10-05 18:46:22 (Show Source):
You can put this solution on YOUR website!Pick two points:
(x,y)
(x 1,y 1)
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m = (y - y 1) / (x - x 1)
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Now you're on your way to defining the equation in slope-intercept form: y = mx+b
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Pick one of your points and substitute for 'x' and 'y' to fine 'b'.
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And you're done.
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Word_Problems_With_Coins/510170: A parking meter costs .50 for one hour. it takes quarters dimes and nickles how many different combinations are there to equal .50
I came up with an answer of 1901 was I close or way off
thank you for your help
Alexis 7th grade
1 solutions
Answer 341739 by oberobic(2304) on 2011-10-05 18:42:41 (Show Source):
You can put this solution on YOUR website!This sort of problem is tedious because you have to find all the possibilities.
50 cents can be 2 quarters, or 1 quarter and 5 nickels, or 1 quarter and 2 dimes and 1 nickel, etc.
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| Q | D | N | Total |
| 2 | 0 | 0 | 50 |
| 1 | 2 | 1 | 50 |
| 1 | 1 | 3 | 50 |
| 1 | 0 | 5 | 50 |
| 0 | 5 | 0 | 50 |
| 0 | 4 | 2 | 50 |
| 0 | 3 | 4 | 50 |
| 0 | 2 | 6 | 50 |
| 0 | 1 | 8 | 50 |
| 0 | 0 | 10 | 50 |
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Rate-of-work-word-problems/510150: Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself?
1 solutions
Answer 341735 by oberobic(2304) on 2011-10-05 18:33:20 (Show Source):
You can put this solution on YOUR website!Work problems are fraction problems in disguise.
Each resource does a fraction of the work per unit of time.
All of the resource fractions total 1 whole job.
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Clarissa can do the job in 5 days less than Shawna.
But we don't now how fast Shawna can do the job.
Hmmm.
We can define Shawna as doing the job in 'S' days.
So she does 1/S of the job per day.
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Clarissa does the job in S-5 days.
So she does 1/(S-5) of the job per day.
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Working together they can do the job in 6 days.
So they can do 1/6 of the job per day.
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(1/S + 1/S-5)*6 = 1 whole job
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(S-5+S)/(S*(S-5)) = 1/6
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(2S -5)/(S^2-5S) = 1/6
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cross multiply
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6*(2S-5) = S^2 -5S
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12S -30 = S^2 -5S
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-30 = S^2 -17S
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0 = S^2 -17S + 30
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0 = (S-2)(S-15)
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So, S = 2 or S = 15.
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But we're told Clarissa can do the job 5 days faster than Shawna.
That means S=2 is a spurious root: It is algebraically correct but nonsensical.
(Compare this to a negative width or length.)
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S = 15
so
C = 10
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Check to see if this is the right answer.
Working together, can they do the whole job in 6 days?
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(1/15 + 1/10)*6 = 1 ??
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(2/30 + 3/30)*6 = (5/30)*6
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(5/30)*6 = 30/30 = 1
.
Correct.
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Answer: Working alone, Clarissa can do the job in 10 days.
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How about that spurious root? Would that work out algebraically?
Let's see.
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S = 2
so
C = -3
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(1/2 + 1/-3)*6 = ??
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(3/6 - 2/6)*6 = 1/6*6 = 6/6 = 1
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Yep. But there is no way for Clarissa to the job in negative 3 days.
.
Done.
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Miscellaneous_Word_Problems/510130: Your club is selling candles to raise money. It costs $100 to rent a booth to sell candles. If the candles cost $1 each and are sold for $5 each, how many candle must be sold to equal your expenses?
1 solutions
Answer 341718 by oberobic(2304) on 2011-10-05 18:10:03 (Show Source):
You can put this solution on YOUR website!Profit = Total Revenue - Total Cost
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Total Cost = Variable Cost per Unit * Number of Units Produced + Fixed Costs
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Total Revenue = Sales Price * Units Sold
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x = number of candles
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TC = $1/candle * x candles + $100
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TR = $5/candle * x
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We want to find the point where TC =TR, which is the break-even point.
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1x + 100 = 5x
100 = 4x
x = 25
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So when you sell 25 candles at $5, you achieve $0 profitability.
Of course, that means you have paid your fixed costs ($100).
In turn that means the rest of your candles sales contribute profit.
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In the following graph, the red line is TC and the green line is TR.
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