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Maths68 answered: 1474 problems
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Expressions-with-variables/550558: the ages of the three brothers are concecutive even integers. three time the age of the youngest brother exceeds the oldest brother age by 48years. what is the age of the youngest brother
1 solutions
Answer 358845 by Maths68(1474)   on 2011-12-27 22:12:38 (Show Source):
You can put this solution on YOUR website!
Let
Age of youngest brother = x+2
Age of elder brother = x+4
Age of oldest brother = x+6
Three time the age of the youngest brother exceeds the oldest brother age by 48years
3(x+2)=(x+6)+48
3x+6=x+6+48
3x+6=x+54
3x-x=54-6
2x=48
2x/2=48/2
x=24
Age of youngest brother = x+2 = 24+2 = 26
Age of elder brother = x+4 = 24+4 = 28
Age of oldest brother = x+6 = 24+6 = 30
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Travel_Word_Problems/549486: How Long would it take to drive a car to the moon at the rate of 65 mph?
1 solutions
Answer 357783 by Maths68(1474) on 2011-12-21 00:32:18 (Show Source):
You can put this solution on YOUR website!Distance from Earth to Moon = 238,857 miles
Speed of car = 65mph
Time = Distance/speed
Time = 238857/65
Time = 3674.723077 hours.
If you drive with a uniform speed of 65mph it will take 3674.723077 hours to get at Moon.
If your are really serious about this idea, don't forget to take me with you!!!!!!!
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Expressions-with-variables/548930: I need help solving systems
-3x + 6y = 24
2x + y =-1
and
-3x + y =5
2x - y =5
1 solutions
Answer 357295 by Maths68(1474) on 2011-12-18 23:15:51 (Show Source):
You can put this solution on YOUR website!-3x + 6y = 24...........(1)
2x + y =-1..............(2)
Multiply (1) by 2 and (2) by 3 and add
-6x+12y=48
6x+3y=-3
-------------------
15y=45
15y/15=45/15
y=3
Put the value of y in (1)
-3x + 6y = 24...........(1)
-3x + 6(3) = 24
-3x + 18 = 24
-3x = 24-18
-3x = 6
-3x/-3 = 6/-3
x=-2
x,y=-2,3
Check
======
Put the value of x and y in (1)
-3x + 6y = 24...........(1)
-3(-2) + 6(3) = 24
6+18=24
24=24
Put the value of x and y in (2)
2x + y =-1..............(2)
2(-2)+3=-1
-4+3=-1
-1=-1
============================================================================================
-3x + y =5...............(1)
2x - y =5................(2)
Add (1) and (2)
-3x + y =5
2x - y =5
-----------------
-x=10
x=-10
Put the value of x in (1)
-3x + y =5...............(1)
-3(-10) + y =5
30+y=5
y=5-30
y=-25
x,y=-10,-25
Check
======
Put the values of x and y in (1)
-3x + y =5...............(1)
-3(-10)+(-25)=5
30-25=25
5=5
Put the values of x and y in (2)
2x - y =5................(2)
2(-10) - (-25) =5
-20+25=5
5=5
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Problems-with-consecutive-odd-even-integers/548889: There are two numbers. the second number is 3 more than the first.the prouduct of the two numbers ia 9 more than teir sum. What are the two numbers?
1 solutions
Answer 357294 by Maths68(1474) on 2011-12-18 23:02:31 (Show Source):
You can put this solution on YOUR website!Let y and x be the first and second numbers
The second number is 3 more than the first
x=y+3..........(1)
The product of the two numbers is 9 more than their sum
xy=(x+y)+9......(2)
Put the value of x from (1) to (2)
(y+3)y=(y+3)+y)+9
y^2+3y=y+3+y+9
y^2+3y=2y+12
y^2+3y-2y-12=0
y^2+y-12=0
y^2+4y-3y-12=0
y^2+4y-3y-12=0
y(y+4)-3(y-4)=0
(y+4)(y-3)=0
y+4=0 or y-3=0
y=-4 or y=3
Put y=3 in (1)
x=y+3..........(1)
y=3
x=3+3
x=6
Put y=-4 in (1)
x=(-4)+3
x=-4+3
x=-1
x,y=6,3 or x,y=-1,-4
Check
=====
Put x,y=(6,3) in (1)
x=y+3..........(1)
6=3+3
6=6
Put x,y=(6,3) in (2)
xy=(x+y)+9......(2)
(6)(3)=(6+3)+9
18=9+9
18=18
Put x,y=(-1,-4) in (1)
x=y+3..........(1)
-1=-4+3..........(1)
-1=-1
Put x,y=(-1,-4) in (2)
xy=(x+y)+9......(2)
(-1)(-4)=(-1-4)+9
4=-5+9
4=4
Numbers are = 3,6 or -4,-1
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�t�e�s�t/548893: if the reciprocal of a number is subtracted from twice the number, the result is 7/2. find the number.
1 solutions
Answer 357287 by Maths68(1474) on 2011-12-18 22:31:49 (Show Source):
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test/548422: Using the elimination process how do you find
-8x+4y=-7
4x-2y=-1
3x+7y=10
5x=7-2y
1 solutions
Answer 356991 by Maths68(1474) on 2011-12-17 12:46:13 (Show Source):
You can put this solution on YOUR website! ..........(1)
 ...........(2)
Multiply by -2 both sides of equation (2)
 ...........(3)
LHS of equation (1) and (3) are same but RHS of both equation is different. It means that values of x and y for both equation are different. Therefore it is impossible to know the value of x and y by solving these two equations.
 .............(1)
 ..............(2)
Multiply (1) by 5 and (2) by 3
 .............(3)
 ..............(4)
Subtract (4) from (3)
.............(3)
 ..............(4)
----------------
Put the value of y in (1)
.............(1)
(x,y)=(1, 1)
Check
------
Put the values of x and y in (1)
.............(1)
Put the values of x and y in (2)
..............(2)
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Inequalities/548263: How do I write the standard form of the equation of the line:
through: (4,4) parallel to y = 1/4x - 5
1 solutions
Answer 356940 by Maths68(1474) on 2011-12-16 22:35:43 (Show Source):
You can put this solution on YOUR website!Given
Point (x, y)=(4,4)
Line:
y=1/4(x)-5
==========================================================
Compare given equation with Equation of line standard form (y=mx+b)
m=1/4
b=-5
Slope of the given line m = 1/4 and y-intercept = b = -5
Since given line is parallel to the required line; slopes of the both line will be same.
================================================================
Now we have a point (4,4) and slope (1/4) of the required line we can easily find the required line by putting these values in the equation of slope-intercept form to find the y-intercept of the required line
y=mx+b
4=(1/4)(4)+b
4=4/4+b
4=1+b
4-1=b
3=b
b=3
y-intercept of the required line =b=3
================================================================
Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form
y=mx+b
y=(x/4)+3
Above equation is the required equation of the line in slope-intercept form.
Graph
Given line = y = x/4 - 5 (Red line)
Required line = y = x/4 +3 (Green line)
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Age_Word_Problems/548009: Aunt Karen is eight years younger than twice the age of Mary. Their ages add up to twenty-eight. Find the ages of Aunt Karen and Mary.
1 solutions
Answer 356841 by Maths68(1474) on 2011-12-16 12:33:17 (Show Source):
You can put this solution on YOUR website!
Let
Present age of Aunt Karen = k
Present age of Mary = m
Aunt Karen is eight years younger than twice the age of Mary
k+8=2m
k=2m-8..........(1)
Their ages add up to twenty-eight.
k+m=28.........(2)
Put the value of k from (1) to (2)
2m-8+m=28
3m=28+8
3m=36
3m/3=36/3
m=12
Put the value of m in (1)
k=2m-8..........(1)
k=2(12)-8
k=24-8
k=16
Present age of Aunt Karen = k = 16
Present age of Mary = m = 12
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Age_Word_Problems/548257: In 12 years time,I shall be three times the age i was 10 years ago, how old am i?
1 solutions
Answer 356832 by Maths68(1474) on 2011-12-16 12:23:24 (Show Source):
You can put this solution on YOUR website!Let
Your present age = x
10 years ago you were = x-10
In 12 years you will be = x+12
According to given condition
x+12=3(x-10)
x+12=3x-30
x-3x=-30-12
-2x=-42
Divide by -2 both sides
-2x/-2=-42/-2
x=21
Your present age = x = 21 years old
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test/548139: the perimeter of a rectangle is 128. the length is 1 m more than twice the width. find the dimension, what is the length and the width
1 solutions
Answer 356731 by Maths68(1474) on 2011-12-15 23:02:21 (Show Source):
You can put this solution on YOUR website!the perimeter of a rectangle is 128. the length is 1 m more than twice the width. find the dimension, what is the length and the width
Length = l=2w+1 m
Width = w
Perimeter = p = 128 m
Perimeter of a Rectangle = length + length + width + width
Perimeter of a Rectangle =2 length +2 width
p = 2l +2w
Put the value of l and p in above equation
128 = 2(2w+1)+2w
128 = 4w+2+2w
128-2=6w
126=6w
Divide by 6 both sides of above equation
126/6=6w/6
21=w
w=21
Given
Length = l=2w+1=2(21)+1=42+1=43m
Dimension of rectangle
p=128
length=43
Width=21
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Numbers_Word_Problems/548135: two consecutive odd numbers are such that three times the first is 5 more than twice the second. What are those two odd numbers?
1 solutions
Answer 356724 by Maths68(1474) on 2011-12-15 22:52:24 (Show Source):
You can put this solution on YOUR website!
Let x+1 is first odd integer
and x+3 is Second odd integer
3 times of the first integer = 3(x+1)
Twice the second integer=2(x+3)
Condition says
three times the first is 5 more than twice the second
3(x+1)=2(x+3)+5
3x+3=2x+6+5
3x-2x=6+5-3
x=8
First odd integer = x+1=8+1=9
Second odd integer = x+3=8+3=11
Check
======
three times the first is 5 more than twice the second
3*9=2*11+5
27=22+5
27=27
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Money_Word_Problems/548124: During a one-month promotional campaign. Video village gave either a free video rental or a 12-serving box of microwave popcorn to new members. It cost the store $1 for each free rental and $2 for each box of popcorn. In all, 48 new members signed up and the store's cost for the incentives was $86. How many of each incentive were given away?
1 solutions
Answer 356721 by Maths68(1474) on 2011-12-15 22:34:18 (Show Source):
You can put this solution on YOUR website!Let
Free Rental given = f
Box of popcorn given = p
Given
------
Cost of Free Rental = $1
Cost of Box of popcorn = $2
Total Cost of incentive = $86
Total incentives given = 48
Free Rental given+Box of popcorn given = Total incentives given
f+p=48
f=48-p...........(1)
(Free Rental given)*(Cost of Free Rental)+(Box of popcorn given)*(Cost of Box of popcorn)= Total Cost of incentive
f*1+p*2=86
f+2p=86............(2)
Put the value of f in (2) from (1)
f+2p=86............(2)
48-p+2p=86
48+p=86
p=86-48
p=38
Put the value of p in (1)
f=48-p...........(1)
f=48-38
f=10
Free Rental given = f = 10
Box of popcorn given = p = 38
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Numbers_Word_Problems/547664: nineteen more than four times a number is equal to the difference between 166 and three times the number. find the number?
1 solutions
Answer 356489 by Maths68(1474) on 2011-12-15 01:41:12 (Show Source):
You can put this solution on YOUR website!Let x be the number
19 more than 4 times x is equal to the 166 minus 3 times x
4x+19=166-3x
4x+3x=166-19
7x=147
7x/7=147/7
x=21
Number is 21
Check
=====
Four times of 21 = 84
Three times of 21 = 21*3=63
Three times 21 + 19 = 166-three times 21
63+19=166-84
82=82
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Equations/547650: A university got a grant worth $250,000. If 35 % of this amount goes to professional development of the staff, how much will be spent for professional development?
1 solutions
Answer 356486 by Maths68(1474) on 2011-12-15 01:33:08 (Show Source):
You can put this solution on YOUR website!Amount will be spent of Professional Development = 250000 * 35%
Amount will be spent of Professional Development = 250000 * 35/100
Amount will be spent of Professional Development = 2500 * 35
Amount will be spent of Professional Development = 87500
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Average/547605: Bill's scores on his first four science tests are 80, 90, 84, and 91. What test score must Bill earn on the fifth test so that his average (mean) is exactly 88?
1 solutions
Answer 356444 by Maths68(1474) on 2011-12-14 22:29:38 (Show Source):
You can put this solution on YOUR website!Total Score in first four tests = 80+90+84+91=345
Score in fifth test = x
Total score in five tests = 345+x
Total number of tests = 5
Average in five test = 88
sum of quantities / number of quantities = Average
(345+x)/5 = 88
345+x=88*5
345+x=440
x=440-345
x=95
Brad has to score 95 in fifth test to get an average of 88.
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Linear_Equations_And_Systems_Word_Problems/547556: Brad wants to buy flowers for his friend with $45. The daisies are $1 each and the roses are $2 each. He buys 3 more daisies than roses. How much did the roses cost?
1 solutions
Answer 356441 by Maths68(1474) on 2011-12-14 22:13:24 (Show Source):
You can put this solution on YOUR website!Let
Brad buys Roses = x
Brad buys Daisies = x+3
Given
1 Rose cost = $2
1 Daisy = $1
Total cost of flowers = 45
Roses*cost of a Rose + Daisies * cost of a Daisy = Total Cost of flowers
x*2+(x+3)*1=45
2x+x+3=45
3x+3=45
3x=45-3
3x=42
3x/3=42/3
x=14
Brad buys Roses = x = 14
Cost of Roses = 14*2=$28
Check
======
Cost of 14 roses = 28
Cost of 17 Daisies = 17
--------------------------
Cost of Flowers = $45
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Numbers_Word_Problems/547030: For two consecutive odd integers, the sum of 3 times the smaller and the larger is 14.
1 solutions
Answer 356184 by Maths68(1474) on 2011-12-14 00:02:35 (Show Source):
You can put this solution on YOUR website!Let
Smaller odd integer = x+1
Larger odd integer = x+3
Given
Sum of 3 time the smaller and the larger is 14
3(x+1)+x+3=14
3x+3+x+3=14
4x+6=14
4x=14-6
4x=8
4x/4=8/4
x=2
Smaller odd integer = x+1 = 2+1 = 3
Larger odd integer = x+3 = 2+3 = 5
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Percentage-and-ratio-word-problems/547031: There are 600 pupils in a school. The ratio of boys to girls in this school is 3:5. How many girls and how many boys are in this school?
Express how. Thanks.
1 solutions
Answer 356182 by Maths68(1474) on 2011-12-13 23:54:06 (Show Source):
You can put this solution on YOUR website!Let
Boys = b
Girls = g
Given
Sum of the boys and girls
g+b=600.......(1)
Ratio of Boys to girls is 3:5
b:g=3:5
b/g=3/5
b=3g/5.........(2)
Put the value of b from (2) to (1)
g+b=600.......(1)
g+3g/5=600
Multiply by 5 both sides of the equation
5(g+3g/5)=5*600
5g+3g=3000
8g=3000
8g/8=3000/8
g=375
Put the value of g in (1)
g+b=600.......(1)
375+b=600
b=600-375
b=225
Boys = b = 225
Girls = g = 375
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Numbers_Word_Problems/547044: The sum of three consecutive integers is 177. What is the largest of the three numbers?
1 solutions
Answer 356180 by Maths68(1474) on 2011-12-13 23:34:38 (Show Source):
You can put this solution on YOUR website!Let x+1, x+2 and x+3 be the three consecutive numbers
Given
The sum of three consecutive integers is 177
x+1+x+2+x+3=177
3x+6=177
3x=177-6
3x=171
3x/3=171/3
x=57
Numbers are
x+1=57+1=58
x+2=57+2=59
x+3=57+3=60
The largest of the three numbers is 60.
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