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# Recent problems solved by 'Maths68'

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 test/522591: A real estate agent received a 5% commission on the sale of a home. If her commission was \$43150 how much did the home sell for?1 solutions Answer 346923 by Maths68(1474)   on 2011-10-27 23:18:07 (Show Source): You can put this solution on YOUR website!Let Home sold for = \$x 5% of x = 43150 5/100 (x) = 43150 5x/100=43150 x/20=43150 x=43150*20 x=863000 Home Sold for \$863000
 test/522575: Find the sales tax and total cost of an item that cost \$109.99 if the tax rate is 7%1 solutions Answer 346921 by Maths68(1474)   on 2011-10-27 23:01:06 (Show Source): You can put this solution on YOUR website!Cost = \$109.99 Sales Tax = 109.99 * 7% = 109.99 * 7/100 = 1.0999 * 7 = 7.6993 = \$7.70 Total Cost = Sales Tax + Cost = 7.70+109.99= \$117.69
 Age_Word_Problems/522189: Mr.Jacobs is 4 times as old as his son. Five years ago, he was 9 times as old as his son. Find Mr.Jacob's age.1 solutions Answer 346723 by Maths68(1474)   on 2011-10-27 12:12:26 (Show Source): You can put this solution on YOUR website!Let Present age of Mr. Jacob = j Present age of Son = s Mr.Jacobs is 4 times as old as his son. j=4s............(1) Five years ago, Mr. Jacob's age = j-5 Son's age = s-5 Then,he was 9 times as old as his son. j-5=9(s-5) j-5=9s-45 j=9s-45+5 j=9s-40............(2) Put the value of j from (1) to (2) 4s=9s-40 4s-9s=-40 -5s=-40 -5s/-5=-40/-5 s=8 Put the value of s in (1) j=4s j=4(8) j=32 Present age of Mr. Jacob = j = 32 years old Present age of Son = s = 8 years old
 Numeric_Fractions/522121: 1 2/3 + (-2 5/6)=1 solutions Answer 346722 by Maths68(1474)   on 2011-10-27 12:06:22 (Show Source): You can put this solution on YOUR website! = = Taking LCM or LCD = = = =
 Coordinate-system/522167: Two points are located at (-3,2) and (1,-1). What is the distance between the points?1 solutions Answer 346718 by Maths68(1474)   on 2011-10-27 11:29:03 (Show Source): You can put this solution on YOUR website!Distance between two points = Points (-3,2) and (1,-1)
 Finance/522154: Simplify. (5 + 3) • 4 1 solutions Answer 346717 by Maths68(1474)   on 2011-10-27 11:16:36 (Show Source): You can put this solution on YOUR website!(5 + 3) • 4 =8*4 =32
 expressions/522153: Evaluate x + y • z if x = 5, y = 8, and z = 2. 1 solutions Answer 346716 by Maths68(1474)   on 2011-10-27 11:14:36 (Show Source): You can put this solution on YOUR website!if x = 5, y = 8, and z = 2. =x+(y*z) =5+(8*2) =5+16 =21
 Finance/522156: Simplify. 3 + 9 • 7 – 8 ÷ 21 solutions Answer 346715 by Maths68(1474)   on 2011-10-27 11:11:31 (Show Source): You can put this solution on YOUR website!= = = =
 Age_Word_Problems/522132: Deanna is twice as old as her brother. If the difference in their ages is 7 years, how old is Deanna?1 solutions Answer 346713 by Maths68(1474)   on 2011-10-27 11:01:11 (Show Source): You can put this solution on YOUR website!Let Present age of Deanna = d Present age of Borther = b Deanna is twice as old as her brother. d=2b .......(1) The difference in their ages is 7 years d-b=7..........(2) Plug in the value of d from (1) to (2) 2b-b=7 b=7 Plug in the value of b in (1) d=2b d=2*7 d=14 Deanna is 14 and her brother is 7 years old
 Geometry_proofs/522090: what is the distance between the points (-4,3) and (3,-1)1 solutions Answer 346688 by Maths68(1474)   on 2011-10-27 07:43:55 (Show Source): You can put this solution on YOUR website!(-4,3) and (3,-1) Distance between two points =
 Functions/522064: I f x + 1 / x = 3 t h a n x 2 + t / x 2 = ?1 solutions Answer 346674 by Maths68(1474)   on 2011-10-27 03:47:23 (Show Source): You can put this solution on YOUR website!I f Then =? = Plug in the value of x in above equation. = = = = =
 Functions/522054: solve for x: y=(800/x)+201 solutions Answer 346656 by Maths68(1474)   on 2011-10-27 01:11:28 (Show Source):
 Percentage-and-ratio-word-problems/522046: Sales tax in certain city is 6.5% of the cost. WHat would the sales tax be on a motorcycle that costs \$850? I need the algebraic expression please1 solutions Answer 346655 by Maths68(1474)   on 2011-10-27 01:01:19 (Show Source): You can put this solution on YOUR website! Sales tax = x Cost of Commodity = c Tax% = t Sales tax = Cost of Commodity * tax% x= c * t x=ct (Required Algebraic expression) Check ===== Sales tax = x = ? Cost of Commodity = c = 850 Tax% = t = 6.5% x=ct x=850 * 6.5% x=850*(6.5/100) x=850*0.065 x=55.25 Sales tax on the motorcycle = \$ 55.25
 Polynomials-and-rational-expressions/522040: factoring 3y^2-36y-1351 solutions Answer 346652 by Maths68(1474)   on 2011-10-27 00:20:11 (Show Source): You can put this solution on YOUR website! or or or or
 Numbers_Word_Problems/522022: Find two consecutive integers such that the square of the second added to the square of twice the first is 424.1 solutions Answer 346648 by Maths68(1474)   on 2011-10-26 23:52:25 (Show Source): You can put this solution on YOUR website!Let Ist Integer = x 2nd Integer = x+1 Use or or or inadmissible Ist Integer = x = 9 2nd Integer = x+1 = 9+1 = 10
 Polynomials-and-rational-expressions/521520: Please help me solve this rational expression: b^-2-c^-2 _________ b^-1+c^-1 This is what I have and where I am stuck 1 - 1 __ ___ b^2 - c^2 ________________ 1 + 1 __ ___ b + c I'm not sure if I approached this problem the right way. Thank you for any help1 solutions Answer 346541 by Maths68(1474)   on 2011-10-26 14:06:21 (Show Source):
 Linear-equations/521575: The slope of the line containing the points (5, 3) and (8, 10) is1 solutions Answer 346536 by Maths68(1474)   on 2011-10-26 13:27:51 (Show Source): You can put this solution on YOUR website!points (5, 3) and (8, 10) Slope = rise in y / rise in x slope = y2-y1/x2-x1 Slope =10-3/8-5 Slope = 7/3
 Polynomials-and-rational-expressions/521572: Please complete the problem just want to see if I did it correctly 6x^3-4x divided by 3x^21 solutions Answer 346534 by Maths68(1474)   on 2011-10-26 13:25:25 (Show Source):
 Linear-equations/521571: whats the slope of a line that passes through the points (-3.5) and (7,10)1 solutions Answer 346531 by Maths68(1474)   on 2011-10-26 13:07:07 (Show Source): You can put this solution on YOUR website!Slope = rise in y / rise in x slope = y2-y1 / x2-x1 Points (-3,5) and (7,10) slope = (10-5)/(7-(-3)) slope = (10-5)/(7+3) slope = 5/10 slope = 1/2
 Money_Word_Problems/521565: bought a cake that cost \$75. The sales-tax rate is 10 percent. What is the total amount she paid for the cake?1 solutions Answer 346529 by Maths68(1474)   on 2011-10-26 13:02:19 (Show Source): You can put this solution on YOUR website!Sales tax=75 * 10% Sales tax=75 * 10/100 Sales tax=75 * 1/10 Sales tax=75/10 Sales tax=7.5 She paid = tax+original price = 7.5+75 = \$82.5
 Polynomials-and-rational-expressions/521506: Please help me solve this multiply or divide as indicated: x^4 / x^3-3x^2 _____ ________ x^2-4 / x^2-5x+6 This is what I have so far x^4 * (x-2)(x-3) ________ _________ (x-2)(x+2) * x^2(x-3) This is what I believe is the answer x^2 _____ x+2 I just want to make sure I simplified and canceled out properly Thank you for any help 1 solutions Answer 346513 by Maths68(1474)   on 2011-10-26 12:38:49 (Show Source):
 Age_Word_Problems/521502: The ancient one is 40 years older than the youngster. 10 years agos, the age of the ancient one was 22 years greater than seven times the age of youngster then. How old are both of them today?1 solutions Answer 346503 by Maths68(1474)   on 2011-10-26 11:48:46 (Show Source): You can put this solution on YOUR website! Let Present age of ancient one = a Present age of youngste = b The ancient one is 40 years older than the youngster a=b+40..........(1) 10 years ago, age of ancient one was = a-10 age of youngste was = b-10 Then,the age of the ancient one was 22 years greater than seven times the age of youngster a-10=7(b-10)+22 a-10=7b-70+22 a=7b-70+22+10 a=7b-70+32 a=7b-38..........(2) Put the value of a from (1) to (2) b+40=7b-38 b-7b=-38-40 -6b=-78 -6b/-6=-78/-6 b=-78/-6 b=13 put the value of b (1) a=b+40 a=13 + 40 a=53 Present age of ancient one = a = 53 years old Present age of youngste = b = 13 years old
 Trigonometry-basics/521457: A=1/2bh. If the area of a certain triangle is 38 square centimeters and the base is 8 centimeters what is the height?1 solutions Answer 346496 by Maths68(1474)   on 2011-10-26 11:02:38 (Show Source): You can put this solution on YOUR website! Height=h=? Area of Triangle = (base*height)/2 Put the values of A and b
 Age_Word_Problems/521120: A sister has 3 younger brothers whose ages are equally spaced. At present the sister's age is equal to the sum of her brothers' ages. Five years ago the sum of the brothers' ages was half the sister's present age and the eldest brother was 4 times as old as the youngest. What are the present ages of the sister and her 3 brothers? I'm using system of equations and I managed to come up with 3 of the equations. I realize I need a 4th one because I have 4 unknown variables. I need help immediately.1 solutions Answer 346482 by Maths68(1474)   on 2011-10-26 09:34:01 (Show Source): You can put this solution on YOUR website! Let Present age of Sister = s Present age of Eldest brother = a Present age of younger brother = b Present age of youngest brother = c At present the sister's age is equal to the sum of her brothers' ages. s=a+b+c...................(1) Five years ago age of Eldest brother was = a-5 age of younger brother was = b-5 age of youngest brother was = c-5 Then the sum of the brothers' ages was half the sister's present age s/2=a-5+b-5+c-5 s/2=a+b+c-15 s =2(a+b+c-15).........(2) Put the value of a+b+c from (1) to (2) s = 2(s-15) s=2s-30 s=30 And the eldest brother was 4 times as old as the youngest a-5=4(c-5) a-5=4c-20 a=4c-15.................(3) Since their ages are equally spaced sum of ages of eldest brother and youngest brother divide by 2 will be equal to the age of younger brother b=(a+c)/2 2b=a+c...................(4) Put the value of 's' and (a+c) in equation (1) s=a+b+c s=(a+c)+b 30=2b+b 30=3b 30/3=3b/3 10=b b=10 Now again put the value of 'b' and 's' in equation (1) 30=a+10+c 30-10=a+c 20=a+c 20-c=a a=20-c...........(5) Put the value of 'a' from (5) to (3) 20-c=4c-15 -c-4c=-15-20 -5c=-35 -5c/-5=-35/-5 c=7 Put the value of 'c' in (3) a=4c-15 a=4(7)-15 a=28-15 a=13 Present age of Sister = s = 30 years old Present age of Eldest brother = a = 13 years old Present age of younger brother = b = 10 years old Present age of youngest brother = c = 7 years old Check ====== 13+10+7= 30 (which is present age of sister) 5 years back ============ age of Eldest brother was = a-5 = 13-5= 8 age of younger brother was = b-5 = 10- 5 = 5 age of youngest brother was = c-5 = 7-5 = 2 8+5+2 = 15 (which is half of the present age of sister) And the eldest brother was 4 times as old as the youngest Eldest brother was 8 which is 4 times of 2.
 Age_Word_Problems/521220: Leticia is 21 years older than Kate, in 2 years, Leticia will be twice as old as Kate. Find Leticia's and Katie's current age?1 solutions Answer 346452 by Maths68(1474)   on 2011-10-26 02:05:28 (Show Source): You can put this solution on YOUR website!Let Present age of Leticia = l Present age of Kate = k Leticia is 21 years older than Kate l=k+21................(1) In 2 years, Leticia's age will be = l + 2 Kate's age will be = k + 2 Then, Leticia will be twice as old as Kate. l + 2 = 2 (k + 2) l + 2 = 2k + 4 l = 2k + 4 - 2 l = 2k + 2 ..................(2) Put the value of l from (1) to (2) k + 21 = 2k + 2 k - 2k = 2 - 21 -k = -19 Multiply by -1 both sides k = 19 Put the value of k in (1) l=k+21 l=19+21 l = 40 Present age of Leticia = l = 40 years old Present age of Kate = k = 19 years old
 Age_Word_Problems/521268: Write an equation to solve this: If my age is 44 and my sisters age is 48 what age will we each be when our total combined age is 150?1 solutions Answer 346450 by Maths68(1474)   on 2011-10-26 01:58:21 (Show Source): You can put this solution on YOUR website!Write an equation to solve this: If my age is 44 and my sisters age is 48 what age will we each be when our total combined age is 150? Let Total Combined age will be 150 after = x years After x years Your age = 44+x Your sister's age = 48+x Sum of ages 44+x+48+x=150 2x+92=150 2x=150-92 2x=58 2x/2=58/2 x=29 After 29 years total combined age will be 150 Your age = 44+x = 44+29 = 73 Your sister's age = 48+x = 48+29 = 77 Your age + Your sisters age = 150 73+77=150 150=150
 Age_Word_Problems/521371: the father was 8 times older than his doughter 4 years ago,in twenty years time the father wil be twice the age of the doughter. 1)how old is the father now? 2)how old wl be the doughter in 30 years time? 1 solutions Answer 346449 by Maths68(1474)   on 2011-10-26 01:36:35 (Show Source): You can put this solution on YOUR website!Let Present age of Father = f Present age of Daughter = d 4 years ago Age of father = f-4 Age of daughter = d-4 Then The father was 8 times older than his daughter f-4=8(d-4) f-4=8d-32 f=8d-32+4 f=8d-28......................(1) In twenty years time Age of father will be = f + 20 Age of daughter will be = d+ 20 Then father will be twice the age of the daughter. f+20=2(d+20) f+20=2d+40 f=2d+40-20 f=2d+20.......................(2) Plug in the value of f from (1) to (2) 8d-28=2d+20 8d-2d=20+28 6d=48 6d/6=48/6 d=8 Put the value of d in (1) f=8d-28 f=8(8)-28 f=64-28 f=36 Present age of Father = f = 36 years old Present age of Daughter = d = 8 years old Daughter will be 38 years old after 30 years.
 Linear-equations/521342: Write an equation of the line contaning the given point and perpendicular to the givin line (3,-6); 4x+9y=71 solutions Answer 346442 by Maths68(1474)   on 2011-10-26 00:09:37 (Show Source): You can put this solution on YOUR website!Given Point (x, y)=(3,-6) Line: 4x+9y=7 Rearrange the equation according to equation of standard form 4x+9y=7 9y=-4x+7 9y/9=(-4x+7)/9 y=(-4/9)x+7/9 Compare above equation with the equation of line slope-intercept form y=mx+b m=-4/9 and b=7/9 Slope of the given line m =-4/9 and y-intercept = b =7/9 Since required line is perpendicular, the multiplication of the slopes of both lines result in (-1), therefore the slope of the required line will be (9/4) ================================================================ Now we have a point (3,-6) and slope (9/4) of the required line we can easily find the required line put these values in the equation of slope-intercept form to find the y-intercept of the required line y=mx+b -6=(9/4)(3)+b -6=27/4+b -6-27/4=b -24-27/4=b -51/4=b b=-51/4 y-intercept of the required line =b=-51/4 ================================================================ Put the values of ‘m’ and ‘b’ in equation of the line slope-intercept form y=mx+b y=(9/4)x-51/4 Above equation is the required equation of the line Red Line = y =(-4/9)x+7/9 Green Line = y =(9/4)x-51/4
 Graphs/520880: How do you graph 10x+6y=-601 solutions Answer 346249 by Maths68(1474)   on 2011-10-25 13:36:08 (Show Source): You can put this solution on YOUR website!10x+6y=-60 6y=-60-10x 6y/6=(-60-10x)/6 y=(-60/6)-(10x/6) y=-(5/3)x-10 y=-5x/3-10
 Travel_Word_Problems/520854: Mr. Anders and Mr. Rich each drove home from a business meeting. Mr. Anders traveled east at 100 kilometer per hour and Ms. Rich traveled west at 80 kilometers per hours. In how many hours were they 100 kilometers apart.1 solutions Answer 346246 by Maths68(1474)   on 2011-10-25 13:25:48 (Show Source): You can put this solution on YOUR website!Effective Speed = 100 + 80 = 180 kmph Distance apart = 100 km Time = Distance / Speed Time = 100 / 180 Time = 0.556 hour After 0.556 hour they will be (approximately)100 kilometers apart. Check ===== Mr. Anders will cover = Speed * time = 100*0.556= 55.60 km Mr. Rich will cover = Speed * time = 80 * 0.556 = 44.48 km After 0.556 hour they will be = 100.08 miles apart.
 Travel_Word_Problems/520806: Two planes leave the airport at the same time. One flies directly east at 540 miles per hour. The other flies west at 720 miles per hour. How long will it take them to be 1890 miles apart?1 solutions Answer 346239 by Maths68(1474)   on 2011-10-25 13:00:03 (Show Source): You can put this solution on YOUR website!Effective Speed = 540+720 = 1260 mph Distance = 1890 miles Time = Distance / Speed Time = 1890/1260 time = 1.5 hour. After 1.5 hours two planes will be 1890 miles apart? Check ====== Plane A Data ============ Speed = 540 mph Time = 1.5 hour Distance covered = ? Distance = Speed * Time Distance covered= 540 * 1.5 = 810 miles Plane B Data ============ Speed = 720 mph Time = 1.5 hour Distance covered = ? Distance = Speed * Time Distance covered = 720 * 1.5 = 1080 miles Total Distance between two planes after 1.5 hours = 1080+810 = 1890 miles