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Maths68 answered: 1474 problems
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Travel_Word_Problems/568956: What is the average of 3/5 and 9/2?
1 solutions

Answer 367181 by Maths68(1474) on 2012-02-07 02:57:07 (Show Source):

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= %283%2F5%2B9%2F2%29%2F2

Numbers_Word_Problems/568951: a number is 5 less than three times another number. the sum of two numbers is 31. Wat r d numbers?
1 solutions

Answer 367180 by Maths68(1474) on 2012-02-07 02:43:27 (Show Source):

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Let
x = larger number
y = smaller number

Given
The sum of two numbers is 31
x+y=31
x=31-y..........(1)
A number is 5 less than three times another number
x=3y-5..........(2)
Put the value of x from (2) to (1)
3y-5=31-y
3y+y=31+5
4y=36
4y/y=36/4
y=9
Put the value of y in (1)
x=31-y
x=31-9
x=22
Numbers are 22 and 9

Money_Word_Problems/568936: On her most recent investment Kristi earned $300 on a total of $2,500 invested. What is her rate of return?
1 solutions

Answer 367176 by Maths68(1474) on 2012-02-07 02:16:04 (Show Source):

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Let
x% of 2500 = 300
%28x%2F100%29%2A2500=300

Divide by 25 both sides of above equation
25x%2F25=300%2F25

cross%2825%29x%2Fcross%2825%29=cross%28300%29%2Fcross%2825%29

Rate of return 12%

Age_Word_Problems/568898: Skyler is 20 years older than Jason. In 8 years, Skyler will be twice as old as Jason. How old is each now?
1 solutions

Answer 367173 by Maths68(1474) on 2012-02-07 02:04:06 (Show Source):

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Let
Present age of Skyler = s
Present age of Jason = j
Given
Skyler is 20 years older than Jason
s=j+20.................(1)
In 8 years
Skyler will be = s+8
Jason will be = j+8
Then
Skyler will be twice as old as Jason
s+8=2(j+8)
s+8=2j+16
s=2j+16-8
s=2j+8..............(2)
Put the value of s from (1) to (2)
j+20=2j+8
j-2j=8-20
-j=-12
Multiply by -1 both sides
(-1)(-j)=(-1)(-12)
j=12
Put the value of j in (1)
s=j+20
s=12+20
s=32

Present age of Skyler = s = 32 years old
Present age of Jason = j = 12 years old

Numbers_Word_Problems/568400: Two thirds of a number is seven more than one fifth of that number. Find the number.
1 solutions

Answer 366951 by Maths68(1474) on 2012-02-06 12:24:00 (Show Source):

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Let
x be the number
2/3(x)=1/5(x)+7
2x/3=x/5+7
2x/3-x/5=7
Take LCD
(2x(5)-x(3))/15=7
10x-3x=7*15
7x=105
7x/7=105/7
x=15
Two thirds of 15 is seven more than one fifth of 15.

Check
Two thirds of 15 = (2/3)(15)=30/3=10
seven more than one fifth of 15 = (1/5)(15)+7=15/5+7=3+7=10

percentage/567677: A desk is on sale for $220.80 , which is 76% less than the regular price.
What is the regular price?

1 solutions

Answer 366663 by Maths68(1474) on 2012-02-04 13:01:11 (Show Source):

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Let
Regular Price = x
Discount = 76% of x = (76/100)(x)
Discount = 76% of x = 76x/100

Regular price - Discount = Sale price
x - 76x/100=220.80
(100x-76x)/100=220.80
24x=220.80*100
24x=22080
24x/24=22080/24
x=920
Regular price is $920

Age_Word_Problems/567656: marilyn is three years younger than her friend rosie. in seven years the product of their ages will be 2 less than six times the product of their ages five years ago. how ald are each at present
1 solutions

Answer 366662 by Maths68(1474) on 2012-02-04 12:46:35 (Show Source):

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Let
Present age of Marilyn = m
Present age of Rosie = r

Marilyn is three years younger than her friend Rosie
m=r-3..............(1)
Five years ago
Age of Marilyn was = m-5
Age of Rosie was = r-5
In seven years
Age of Marilyn will be = m+7
Age of Rosie will be = r+7
THEN
In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.
(m+7)(r+7)=6[(m-5)(r-5)]-2
mr+7m+7r+49=6(mr-5m-5r+25)-2
mr+7m+7r+49=6mr-30m-30r+150-2
mr-6mr+7m+30m+30r+7r=150-2-49
-5mr+37m+37r=150-51
-5mr+37m+37r=99..................(2)
Put the value of m from (1) to (2)
-5(r-3)r+37(r-3)+37r=99
-5r^2+15r+37r-111+37r=99
-5r^2+89r-99-111=0
-5r^2+89r-200=0
Now solve for r

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ar%5E2%2Bbr%2Bc=0

(in our case -5r%5E2%2B89r%2B-210+=+0

) has the following solutons:

r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

b%5E2-4ac=%2889%29%5E2-4%2A-5%2A-210=3721

.

Discriminant d=3721 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-89%2B-sqrt%28+3721+%29%29%2F2%5Ca

r%5B1%5D+=+%28-%2889%29%2Bsqrt%28+3721+%29%29%2F2%5C-5+=+2.8

r%5B2%5D+=+%28-%2889%29-sqrt%28+3721+%29%29%2F2%5C-5+=+15

Quadratic expression -5r%5E2%2B89r%2B-210

can be factored:
-5r%5E2%2B89r%2B-210+=+-5%28r-2.8%29%2A%28r-15%29

Again, the answer is: 2.8, 15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B89%2Ax%2B-210+%29

r=15 or r = 2.8 (reject)
Put r=15 in (1)
m=r-3
m=15-3
m=12

Present age of Marilyn = m = 12 years old
Present age of Rosie = r = 15 years old

Check
======
Five years ago
Age of Marilyn was = 7
Age of Rosie was = 10
In seven years
Age of Marilyn will be = 19
Age of Rosie will be = 22
THEN
In seven years the product of their ages will be 2 less than six times the product of their ages five years ago.
19*22=6(7*10)-2
418=6(70)-2
418=420-2
418=418

Equations/567646: If 20% of a company's 5,000 employees will retire in the next ten years, how many will NOT retire?
1 solutions

Answer 366660 by Maths68(1474) on 2012-02-04 12:04:14 (Show Source):

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Retire = 20%
Not retire = 100%-20%=80%
80% of 5000 = (80%)(5000)
80% of 5000 = (80/100)(5000)
80% of 5000 = (80)(50)
80% of 5000 = 4000
4000 will not retire.

Percentage-and-ratio-word-problems/567386: 8% of what number is 72?
1 solutions

Answer 366520 by Maths68(1474) on 2012-02-03 13:19:12 (Show Source):

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8% of what number is 72

Let
72 is 8% of x
8%x=72
(8/100)(x)=72
(2/25)(x)=72
2x/25=72
2x=72*25
2x=1800
2x/2=1800/2
x=900

72 is 8% of 900

Numbers_Word_Problems/567383: one dozen doughnuts cost $2.59 while 5 doughnuts cost $13.39. which is the better buy?
1 solutions

Answer 366519 by Maths68(1474) on 2012-02-03 13:12:13 (Show Source):

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Cost of a doughnuts at 2.59 per dozen = 2.59/12 = 0.215833
Cost of a doughnuts at 13.39 per 5 doughnuts = 13.39/5 = 2.678
Buy doughnuts at 2.59 per dozen its a better deal.

Matrices-and-determiminant/567371: There were 510 people at a play. The admission price was 2 for adults and 1 for children. The admission receipts were 810. How many adults and how many children attended?
1 solutions

Answer 366518 by Maths68(1474) on 2012-02-03 12:49:58 (Show Source):

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Let
Adults = x
Children = 510-x
Total receipts = 810

Admission price for Adults = 2
Admission price for Children = 1

(Admission price for Adults)(Adults)+ (Admission price for Children)(Children) = Total receipts
(2)(x)+(1)(510-x)=810
2x+510-x=810
x=810-510
x=300

Adults = x = 300
Children = 510-x = 510-300 = 210

Check
======
300*2+210*1=810
600+210=810
810=810

Volume/567316: I have a box that measures 3m x 3m x 3m. What is the volume of the cube?
1 solutions

Answer 366516 by Maths68(1474) on 2012-02-03 12:36:42 (Show Source):

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Volume of the cube = 3%2A3%2A3

Volume of the cube = 27m%5E3

Money_Word_Problems/567320: If we need to bill $509,375 after subtracting a 10% discount, how much does the original total bill need to be?
1 solutions

Answer 366515 by Maths68(1474) on 2012-02-03 12:29:09 (Show Source):

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Let
Original bill = $x

10% of x = 10/100 (x)
10% of x = 1/10 (x)
10% of x = x/10
Bill = original bill - 10% discount
509375=x-x/10
509375=(10x-x)/10
10* 509375=(10x-x)
5093750=9x
5093750/9=9x/9
565972.20=x
x=565972.20
Original bill = $565972.20

Money_Word_Problems/567339: A salary after a 4.5% increase, if the original salary is x dollars
1 solutions

Answer 366514 by Maths68(1474) on 2012-02-03 12:15:56 (Show Source):

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Salary = x dollars
Increase =4.5% of x
Increase =(4.5/100)x
Increase =0.045x

Salary after increase = Salary Increase + Salary
Salary after increase = 0.045x + x
Salary after increase = 1.045x

Example
========
Let Salary = 4000
4.5% of 4000 = 4.5/100(4000)
4.5% of 4000 = 4.5(40)
4.5% of 4000 = 4.5(40)
4.5% of 4000 = 180
Salary after increase = 180 + 4000
Salary after increase = 4180

Now put salary in the following formula
Salary after increase = 1.045x
Salary after increase = 1.045(4000)
Salary after increase = 4180

Polynomials-and-rational-expressions/567158: multiply and simplify 10x^5/3q^3 times 9q^5/100x
1 solutions

Answer 366465 by Maths68(1474) on 2012-02-02 23:11:59 (Show Source):

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= %2810x%5E5%2F3q%5E3%29%289q%5E5%2F100x%29

%28%28x%29%28x%29%28x%29%28x%29%2F1%29%283q%2F10%29

Numeric_Fractions/567164: what is 12 and 1/3 subtract 7 and 5/6
1 solutions

Answer 366441 by Maths68(1474) on 2012-02-02 21:36:28 (Show Source):

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= %2812%261%2F3%29-%287%265%2F6%29

Take LCD
= %28%2837%29%282%29-%2847%29%281%29%29%2F6

Mixture_Word_Problems/566596: How many gallons of 20% alcohol must be mixed with 3 gallons of 70% alcohol to get a mixture that is 30% alcohol
1 solutions

Answer 366285 by Maths68(1474) on 2012-02-02 00:42:04 (Show Source):

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Solution A
Amount =x gallons
Concentration =20% = 0.2
Solution B
Amount = 3 gallons
Concentration =70% = 0.70
Resultant Solution
Amount =(x+3)gallons
Concentration = 30% = 0.3

[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Resultant * Concentration of resultant
(x)(0.2)+(3)(0.7)=(x+3)(0.3)
0.2x+2.1=0.3x+0.9
0.2x-0.3x=0.9-2.1
-0.1x=-1.2
-0.1x/-0.1=-1.2/-0.1
x=12

Solution A
Amount = x = 12 gallons
Concentration =20% = 0.2

12 gallons of 20% alcohol must be mixed with 3 gallons of 70% alcohol to get a 15 gallons of mixture that is 30% alcohol

Polynomials-and-rational-expressions/566593: Evaluate each polynomial for x = 3 and for x = −3.
−x^(2) − 3x^(3) − x^(4)

1 solutions

Answer 366283 by Maths68(1474) on 2012-02-02 00:34:25 (Show Source):

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= -x%5E2-3x%5E3-x%5E4

x=-3
=

-%28-3%29%5E2-3%28-3%29%5E3-%28-3%29%5E4

x=3
=

Human-and-algebraic-language/566588: The difference in five times a number and eight times another number. Translate into a variable expression and simplify if possible.
1 solutions

Answer 366274 by Maths68(1474) on 2012-02-02 00:14:23 (Show Source):

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Let
x and y are two numbers
The difference in five times a number and eight times another number
Translation=5x-8y

Square-cubic-other-roots/566573: Evaluate What is the square root of b^2-4ac where a=2, b=-5, and c=-3
1 solutions

Answer 366272 by Maths68(1474) on 2012-02-01 23:28:18 (Show Source):

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= sqrt%28b%5E2-4ac%29

a=2, b=-5, and c=-3
= sqrt%28%28-5%29%5E2-4%282%29%28-3%29%29

Expressions-with-variables/566566: Solve this question using substitution y=5x+5 y=15x-1
1 solutions

Answer 366270 by Maths68(1474) on 2012-02-01 23:17:33 (Show Source):

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y=5x%2B5

........(1)
y=15x-1

.......(2)
Substitute the value of y from (2) to (1)
15x-1=5x%2B5

cross%2810%29x%2Fcross%2810%29=cross%286%29%2Fcross%2810%29

Put the value of x in (1)
y=5x%2B5

........(1)
y=5%283%2F5%29%2B5

y=cross%285%29%283%2Fcross%285%29%29%2B5

x,y = 3/5, 8

Check
=====
Put the value of x and y in (1)
y=5x%2B5

........(1)
8=5%283%2F5%29%2B5

8=cross%285%29%283%2Fcross%285%29%29%2B5

Put the value of x and y in (2)
y=15x-1

Mixture_Word_Problems/566568: my question:
A chemist mixes 12l of a solution tht is 45% acid wiht 8l of a sotution that is 70 % acid, what is the % of acid of the mixture?
1 solutions

Answer 366269 by Maths68(1474) on 2012-02-01 23:06:56 (Show Source):

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Solution A
Amount =121
Concentration =45% = 0.45
Solution B
Amount = 81
Concentration =70% = 0.70
Mixture
Amount =(81+121)=202
Concentration =x
[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Mixture * Concentration of Mixture
(121)(0.45)+(81)(0.70)=(202)(x)
54.45+56.70=202x
111.15=202x
111.15/202=202x/202
0.550248=x
x=0.550248

Mixture
Amount =(81+121)=202
Concentration =x = 0.550248 = 0.550248/100 = 55.0248%

Chemist will have 202 of 55.0248% acid mixture.

test/566537: 10 - 6v = -104
1 solutions

Answer 366268 by Maths68(1474) on 2012-02-01 22:56:20 (Show Source):

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10-6v=-104

Add 6v and 104 both sides of the equation
10-6v%2B6v%2B104=-104%2B104%2B6v

10-cross%286v%29%2Bcross%286v%29%2B104=-cross%28104%29%2Bcross%28104%29%2B6v

Divide by 6 both sides of above equation
114%2F6=6v%2F6

cross%28114%29%2Fcross%286%29=cross%286%29v%2Fcross%286%29

Check
=====
10-6v=-104

Put v=19

Proportions/566552: What is 'x' in 20-x/x=6/4
1 solutions

Answer 366267 by Maths68(1474) on 2012-02-01 22:47:33 (Show Source):

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%2820-x%29%2Fx=6%2F4

%2820-x%29%2Fx=cross%286%29%2Fcross%284%29

cross%2840%29%2Fcross%285%29=cross%285%29x%2Fcross%285%29

Check
=====
%2820-x%29%2Fx=6%2F4

Put x=8

cross%2812%29%2Fcross%288%29=cross%286%29%2Fcross%284%29

Travel_Word_Problems/566555: Luis walked one - eighth of the distance to school.What part of the distance to school does he still need to walk?
1 solutions

Answer 366263 by Maths68(1474) on 2012-02-01 22:34:02 (Show Source):

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Let
Total Distance = x
Luis walked one-eighth of x = x(1/8) = x/8
He still need to walk = Total Distance - Distance covered
He still need to walk = x-x/8
He still need to walk = (8x-x)/8
He still need to walk = 7x/8
He still need to walk = x(7/8)
He still need to walk seven-eighth of the total distance.

Linear_Algebra/566535: The sum of two numbers is 30. The larger number is 5 more than four times the smaller one. Find the product of the number. (Ans 125)
1 solutions

Answer 366247 by Maths68(1474) on 2012-02-01 21:46:44 (Show Source):

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Let
Smaller number = y
Larger number = x

The sum of two numbers is 30
x+y=30..........(1)
The larger number is 5 more than four times the smaller one
x=4y+5..........(2)
Put the value of x from (2) to (1)
x+y=30..........(1)
4y+5+y=30
5y+5=30
5y=30-5
5y=25
5y/5=25/5
y=5
Put the value of y in (2)
x=4y+5..........(2)
x=4(5)+5
x=20+5
x=25

Smaller number = y = 5
Larger number = x = 25
Product of two numbers = 5*25 = 125

test/566521: 3a²-13a+4
1 solutions

Answer 366242 by Maths68(1474) on 2012-02-01 21:36:21 (Show Source):

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= 3a%5E2-13a%2B4

percentage/566527: Hank has some 60% maple syrup and some 100% maple syrup in his restaurant. How many ounces of EACH should he use to make 100 ounces of 85% maple syrup
1 solutions

Answer 366241 by Maths68(1474) on 2012-02-01 21:32:41 (Show Source):

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Solution A
Amount =x ounces
Concentration =60% = 0.6
Solution B
Amount = 100-x ounces
Concentration =100% = 1
Resultant Solution
Amount =100 ounces
Concentration =85%=0.85
[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Resultant * Concentration of resultant
(x)(0.6)+(100-x)(1)=(100)(0.85)
0.6x+100-x=85
-0.4x=85-100
-0.4x=-15
-0.4x/-0.4=-15/-0.4
x=37.5

Solution A
Amount = x = 37.5 ounces
Concentration =60% = 0.6
Solution B
Amount = 100-x = 100-37.5 = 62.5 ounces
Concentration =100% = 1

Hank has to mix 37.5 ounces of 60% maple syrup and 62.5 ounces of 100% maple syrup to make 100 ounces of 85% maple syrup

Functions/566526: I have no idea how to solve this problem and i need help.
f(6)=2/6-2
1 solutions

Answer 366236 by Maths68(1474) on 2012-02-01 21:20:32 (Show Source):

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Equation is not clearly written
However, if it is as follows
f%286%29=2%2F6-2

Take LCD

Or
If equation is as follows
f%286%29=2%2F%286-2%29

Numeric_Fractions/565930: what is 13 4/7 minus 9 9/14
1 solutions

Answer 366043 by Maths68(1474) on 2012-02-01 04:16:51 (Show Source):

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= 13%264%2F7-9%269%2F14

Take LCD
= %28%2895%29%282%29-135%29%2F14

Age_Word_Problems/565367: Ruby is thrice as old as Jade. Jade is 4 years older than Pearl. In ten years Ruby will be 2 years more than twice as old as Jade will then be. How old are they now?
1 solutions

Answer 366026 by Maths68(1474) on 2012-02-01 00:23:28 (Show Source):

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Ruby is thrice as old as Jade. Jade is 4 years older than Pearl. In ten years Ruby will be 2 years more than twice as old as Jade will then be. How old are they now?
Let
Present age of Ruby = r
Present age of Jade = j
Present age of Pearl = p

Ruby is thrice as old as Jade
r=3j............(1)
Jade is 4 years older than Pearl
j=p+4...........(2)

In ten years
Ruby will be = r+10
Jade will be = j+10

Then

Ruby will be 2 years more than twice as old as Jade will be then
r+10=2(j+10)+2
r+10=2j+20+2
r+10=2j+22
r=2j+22-10
r=2j+12.............(3)
Put the value of r from (1) to (3)
3j=2j+12
3j-2j=12
j=12
Put the value of j in (2)
j=p+4...........(2)
12=p+4
p+4=12
p=12-4
p=8
Put the value of j in (1)
r=3j
r=3(12)
r=36

Present age of Ruby = r = 36 years old
Present age of Jade = j = 12 years old
Present age of Pearl = p = 8 years old

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