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# Recent problems solved by 'Maths68'

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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): You can put this solution on YOUR website!= = = = = =
 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): You can put this solution on YOUR website!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): You can put this solution on YOUR website!Let x% of 2500 = 300 Divide by 25 both sides of above equation 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): You can put this solution on YOUR website!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): You can put this solution on YOUR website!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): You can put this solution on YOUR website!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):
You can put this solution on YOUR website!
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 (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=3721 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.8, 15. Here's your graph:

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): You can put this solution on YOUR website!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): You can put this solution on YOUR website!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): You can put this solution on YOUR website!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.
 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): You can put this solution on YOUR website!Volume of the cube = Volume of the cube =
 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): You can put this solution on YOUR website!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 dollars1 solutions Answer 366514 by Maths68(1474)   on 2012-02-03 12:15:56 (Show Source): You can put this solution on YOUR website!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^5/100x1 solutions Answer 366465 by Maths68(1474)   on 2012-02-02 23:11:59 (Show Source): You can put this solution on YOUR website!= = = = = =
 Numeric_Fractions/567164: what is 12 and 1/3 subtract 7 and 5/61 solutions Answer 366441 by Maths68(1474)   on 2012-02-02 21:36:28 (Show Source): You can put this solution on YOUR website!= = Take LCD = = = = = =
 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% alcohol1 solutions Answer 366285 by Maths68(1474)   on 2012-02-02 00:42:04 (Show Source): You can put this solution on YOUR website!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): You can put this solution on YOUR website!= x=-3 = = = = = = 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): You can put this solution on YOUR website!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=-31 solutions Answer 366272 by Maths68(1474)   on 2012-02-01 23:28:18 (Show Source): You can put this solution on YOUR website!= a=2, b=-5, and c=-3 = = = = = or
 Expressions-with-variables/566566: Solve this question using substitution y=5x+5 y=15x-11 solutions Answer 366270 by Maths68(1474)   on 2012-02-01 23:17:33 (Show Source): You can put this solution on YOUR website!........(1) .......(2) Substitute the value of y from (2) to (1) Put the value of x in (1) ........(1) x,y = 3/5, 8 Check ===== Put the value of x and y in (1) ........(1) Put the value of x and y in (2)
 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): You can put this solution on YOUR website!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 = -1041 solutions Answer 366268 by Maths68(1474)   on 2012-02-01 22:56:20 (Show Source): You can put this solution on YOUR website! Add 6v and 104 both sides of the equation Divide by 6 both sides of above equation Check ===== Put v=19
 Proportions/566552: What is 'x' in 20-x/x=6/41 solutions Answer 366267 by Maths68(1474)   on 2012-02-01 22:47:33 (Show Source): You can put this solution on YOUR website! Check ===== Put x=8
 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): You can put this solution on YOUR website!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): You can put this solution on YOUR website!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: 3aČ-13a+41 solutions Answer 366242 by Maths68(1474)   on 2012-02-01 21:36:21 (Show Source): You can put this solution on YOUR website!= = = =
 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 syrup1 solutions Answer 366241 by Maths68(1474)   on 2012-02-01 21:32:41 (Show Source): You can put this solution on YOUR website!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)=2/6-21 solutions Answer 366236 by Maths68(1474)   on 2012-02-01 21:20:32 (Show Source): You can put this solution on YOUR website!Equation is not clearly written However, if it is as follows Take LCD Or If equation is as follows
 Numeric_Fractions/565930: what is 13 4/7 minus 9 9/141 solutions Answer 366043 by Maths68(1474)   on 2012-02-01 04:16:51 (Show Source): You can put this solution on YOUR website!= = Take LCD = = = = =