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# Recent problems solved by 'Maths68'

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 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
 Equations/520858: Half the number y is equal to y minus ten.1 solutions Answer 346238 by Maths68(1474)   on 2011-10-25 12:43:12 (Show Source): You can put this solution on YOUR website!Half the number y is equal to y minus ten. 1/2(y)=y-10 y/2=y-10 2*(y/2)=2*(y-10) y=2y-20 y-2y=-20 -y=-20 Multiply by -1 both sides y=20
 Graphs/520792: find equestion of the line which is perpindicular the line y=5x+9 and has y-intercept=61 solutions Answer 346235 by Maths68(1474)   on 2011-10-25 12:24:07 (Show Source): You can put this solution on YOUR website! find equestion of the line which is perpindicular the line y=5x+9 and has y-intercept=6 Given y=5x+9 Compare above equatoin with Standard Equation of the Straight line y=mx+b Slope m = 5 Since lines are perpendicular, multiplication of their slopes will result in (-1) therefore slope of the required line is (-1/5) and we have been given y-intercept 6 of the required line y=-(1/5)x+6 y=-x/5+6 Above equation is the equatoin of the required line. Red line = Given Line Green line = Required Line
 Age_Word_Problems/520238: John is 10 years older than Chris. In 2 years John will be twice as old as Chris. How old are they now?1 solutions Answer 346199 by Maths68(1474)   on 2011-10-25 07:51:37 (Show Source): You can put this solution on YOUR website!Let Present age of John = j Present age of Chris = c John is 10 years older than Chris. j=c+10 ..........(1) In 2 years John will be = j + 2 Chris will be = c + 2 Then, John will be twice as old as Chris. j + 2 = 2(c + 2) j + 2 = 2c + 4 j = 2c + 4 - 2 J = 2c + 2 .............(2) Put the value of j from (1) to (2) c+10 = 2c + 2 .............(2) c-2c=2-10 -c=-8 Multiply by -1 both sides c=8 Put the value of c in (1) j = 8 + 10 j = 18 Present age of John = j = 18 years old Present age of Chris = c = 8 years old
 Age_Word_Problems/520289: Dorthy is 14 years youngfer than Rita. Ten years ago Rita was 3 times as old as Dorthy was then. How old is each now?1 solutions Answer 346198 by Maths68(1474)   on 2011-10-25 07:45:19 (Show Source): You can put this solution on YOUR website!Let Present age of Dorthy = d Present age of Rita = r Dorthy is 14 years younger than Rita. d=r-14.........(1) Ten years ago Dorthy age was = d-10 Rita age was = r-10 Then, Rita was 3 times as old as Dorthy r-10=3(d-10) r-10=3d-30 r=3d-30+10 r=3d-20...........(2) Plug in the value of d from (1) to (2) r=3(r-14)-20 r=3r-42-20 r-3r=-62 -2r=-62 -2r/-2=-62/-2 r=31 Pulg in the value of r in (1) d=r-14 d=31-14 d=17 Present age of Dorthy = d = 17 years old Present age of Rita = r = 31 years old
 Age_Word_Problems/520370: Six years ago,bill was 1/4 as old as he is now.How old is bill?1 solutions Answer 346189 by Maths68(1474)   on 2011-10-25 05:26:29 (Show Source): You can put this solution on YOUR website!Let Present age of Bill = x Six year ago he was = x-6 Then Bill was 1/4 of his present age 1/4x=x-6 x/4=x-6 x=4(x-6) x=4x-24 x-4x=-24 -3x=-24 -3x/-3=-24/-3 x=8 Bill is 8 years old Check ====== Bill present age 8 years Six years ago = 8-6 = 2 (which is 1/4 of 8)
 Money_Word_Problems/520695: A businessman borrowed from two moneylenders a sum of rs 2000.for 1 loan the rate of simple interest was 8% Pa and the other was 6 % pa he paid total interest of rs 136 for one year .find the sum borrowed on each rate by him ?1 solutions Answer 346188 by Maths68(1474)   on 2011-10-25 05:18:23 (Show Source): You can put this solution on YOUR website!Amount taken at 8% = x Amount taken at 6% = 2000-x Total interest paid = 136 Amount taken * interest rate + Amount taken * interest rate = Total interest paid x*8% + (2000-x)*6% = 136 x*8/100 + (2000-x)*6/100 = 136 Multiply by 100 both sides x*8 + (2000-x)*6 = 136 * 100 8x + 12000-6x=13600 8x - 6x=13600-12000 2x=1600 2x/2=1600/2 x=800 Amount taken at 8% = x = 800 Amount taken at 6% = 2000-x = 2000-800 = 1200 Check 800 * 8/100 + 1200 * 6/100 = 136 8*8 + 12*6 = 136 64+72 = 136 136=136
 Problems-with-consecutive-odd-even-integers/520673: The product of two consecutive odd whole numbers is one less than five times their sum. Find the whole numbers1 solutions Answer 346166 by Maths68(1474)   on 2011-10-25 01:10:45 (Show Source): You can put this solution on YOUR website!Let One odd integer = x+1 Other odd integer = x+3 Given Condition (x+1)(x+3)=5((x+1)+(x+3))-1 x^2+3x+x+3=5(x+1+x+3)-1 x^2+4x+3=5(2x+4)-1 x^2+4x+3=10x+20-1 x^2+4x+3=10x+19 x^2+4x-10x+3-19=0 x^2-6x-16=0 x^2-8x+2x-16=0 x(x-8)+2(x-8)=0 (x-8)(x+2)=0 x-8=0 or x+2=0 x=8 or x=-2 (inadmissible) x=8 One odd integer = x+1 = 8+1=9 Other odd integer = x+3 = 8+3 = 11 Check ====== Product of integers = 5 (sum of integers) -1 9*11=5(9+11)-1 99=5(20)-1 99=100-1 99=99
 Average/520672: two investments were made totaling 8800 dollars. for a certain year these investments yielded 1326 dollars in simple intrest. part of the 8800 was ivested at 14% and part at 16%. Find the amount invested in each rate1 solutions Answer 346165 by Maths68(1474)   on 2011-10-25 00:34:01 (Show Source): You can put this solution on YOUR website!Let Amount invested at 14% = x Amount invested at 16% = 8800-x Given Total interest on both investments = 1326 14% * (x) + 16% * (8800-x) = 1326 14/100 * (x) + 16/100 * (8800-x) = 1326 Multiply by 100 both sides 14 * (x) + 16 * (8800-x) = 1326 * 100 14x + 140800-16x = 132600 -2x=132600-140800 -2x=-8200 -2x/-2=-8200/-2 x=4100 Amount invested at 14% = x = 4100 Amount invested at 16% = 8800-x = 8800-4100 = 4700 Check ===== 4100 * 14/100 + 4700 * 16/100 = 1326 Multiply by 100 both sides 4100*14 + 4700*16 = 132600 57400+75200=132600 132600=132600
 Complex_Numbers/520586: how to solve x+3y=11,x+4y=141 solutions Answer 346142 by Maths68(1474)   on 2011-10-24 22:35:38 (Show Source): You can put this solution on YOUR website!x+4y=14 ..........(1) x+3y=11 ..........(2) Subtract (2) from (1) x+4y=14 -x-3y=-11 -------------- y=3 Plug in the value of y in (1) x+4y=14 x+4(3)=14 x+12=14 Subtract 12 from both sides x+12-12=14-12 Cancel out 12 from Left Hand Side (LHS) x=2 x,y = 2, 3 Check ====== Plug in the values of x and y in (1) x+4y=14 ..........(1) 2+4(3)=14 2+12=14 14=14 Now Plug in the values of x and y in (2) x+3y=11 ..........(2) 2+3(3)=11 2+9=11 11=11
 test/520605: 2r-6=01 solutions Answer 346137 by Maths68(1474)   on 2011-10-24 22:24:38 (Show Source): You can put this solution on YOUR website!2r-6=0 Add 6 both sides 2r-6+6=6 Cancel out 6 from LHS 2r=6 divide by 2 both sides 2r/2=6/2 r=3 Check ====== 2r-6=0 2(3)-6=0 6-6=0 0=0
Exponents/520600: I am suppose to reduce
15x^3/6x^-3
Would the answer be 5x^6/2 ?
1 solutions

Answer 346132 by Maths68(1474)   on 2011-10-24 22:18:51 (Show Source):
You can put this solution on YOUR website!
Yes, you are right.

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: Graphical form: simplifies to Text form: 15x^3/6/x^-3 simplifies to 5*x^(6)/2Cartoon (animation) form: For tutors: `simplify_cartoon( 15x^3/6/x^-3 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Factors 15 and 6 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes .

Look at .
Reduce similar several occurrences of to
It becomes .

Look at .
It becomes .

Look at .
It becomes .
Result:

### Universal Simplifier and Solver

Done!

 Pythagorean-theorem/520172: if you have a right triangle that has a height of 5cm and length of 6cm what is the length of the diagonal1 solutions Answer 345950 by Maths68(1474)   on 2011-10-24 12:57:23 (Show Source): You can put this solution on YOUR website!a = 5cm b = 6cm c = ? Use Pythagorean Theorem c^2=a^2+b^2 c^2=(5)^2+(36)^2 c^2 = 25 +36 c^2 = 61 Taking sqrt both sides sqrtc^2 = sqrt61 c=7.81cm The length of diagonal is 7.81cm
 Linear-equations/520131: find the equation for the line that is parallel to the line wih the equation (y+2)=1/2 (x-4) passing through the point (1,3)1 solutions Answer 345949 by Maths68(1474)   on 2011-10-24 12:49:05 (Show Source): You can put this solution on YOUR website! Standard Form of Equation of the line: y=mx+b Given (y+2)=1/2 (x-4) rearrage the above equation according to the standard form y+2=(1/2)x-4(1/2) y+2=(1/2)x-2 y=(1/2)x-2-2 y=(1/2)x-4 Compare above equation with the standard form equation m=1/2 and b=-4 Since lines are parallel their slopes will be equal,therefore slope of the required line will be (1/2) Now we have a point(1,3) and slope (1/2)of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form. m=(y2-y1)/(x2-x1) 1/2=(y-3))/(x-1) 1*(x-1)=2(y-3) x-1=2y-6 x-1+6=2y x+5=2y 2y=x+5 2y/2=(x+5)/2 y=(1/2)x+5/2 Above equation is the Equation of Staright line in the Standard Form.
 test/520144: Ce nter City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1221 cars, find the capacity for each garage1 solutions Answer 345943 by Maths68(1474)   on 2011-10-24 12:30:09 (Show Source): You can put this solution on YOUR website!Ce nter City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1221 cars, find the capacity for each garage Let The Capacity of Center City West Parking = x The Capacity of Center City East Parking = x + 251 Parking Capacity of Both Centres = Total Parking Capacity x+x+251=1221 2x+251=1221 2x=1221-251 2x=970 2x/2=970/2 x=485 The Capacity of Center City West Parking = x = 485 The Capacity of Center City East Parking = x + 251 = 485+251=736 Check ===== Parking Capacity of Both Centres = Total Parking Capacity 485+736=1221 1221=1221
 Exponents/520157: -3x+2=7x-221 solutions Answer 345941 by Maths68(1474)   on 2011-10-24 12:19:45 (Show Source): You can put this solution on YOUR website!-3x+2=7x-22 -3x-7x=-22-2 -10x=-24 -10x/-10=-24/-10 x=12/5 Check ==== -3(12/5)+2=7(12/5)-22 (-36+10)/5=(84/5)-22 -26/5=(84-110)/5 -26/5=-26/5
 Linear_Equations_And_Systems_Word_Problems/520149: A 68 foot pipe is cut into two pieces, one of the which is 12 ft less than the other. What is the length of the shorter piece?1 solutions Answer 345938 by Maths68(1474)   on 2011-10-24 12:11:18 (Show Source): You can put this solution on YOUR website!A 68 foot pipe is cut into two pieces, one of the which is 12 ft less than the other. What is the length of the shorter piece? Let One piece = x Other piece = x-12 Sum of two pieces = Total length of entire piece x+x-12=68 2x-12=68 2x=68+12 2x=80 x=80/2 x=40 One piece = x = 40 feet Other piece = x-12 = 40-12 = 28 feet Shorter piece = 28 feet
 Geometry_Word_Problems/520153: The width of a rectangle is 4 more than the length,l. write an equation to describe the perimeter in term of w.1 solutions Answer 345935 by Maths68(1474)   on 2011-10-24 12:04:53 (Show Source): You can put this solution on YOUR website!The width of a rectangle is 4 more than the length,l. write an equation to describe the perimeter in term of w. Perimeter = p Lenght = l Width = w Given l+4=w l=w-4 Perimeter = p = 2 length + 2 width p=2l+2w p=2(w-4)+2w p=2w-8+2w p=4w-8 Perimeter in term of w
 Money_Word_Problems/520137: Bernadette inherited \$15,000 and invested it in two municipal bonds, which pay 7 percent and 9 percent simple interest. the annual interest is \$1230. Find the amount at each rate.1 solutions Answer 345934 by Maths68(1474)   on 2011-10-24 11:59:13 (Show Source): You can put this solution on YOUR website! Let Amount invested at 7% = x Amount invested at 9% = 15000-x Given Total interest on both investments = 1230 7% * (x) + 9% * (15000-x) = 1230 7/100 * x + 9/100 * (15000-x) = 1230 Multiply by 100 both sides 7*x + 9 * (15000-x) = 1230 * 100 7x+ 135000-9x = 123000 7x-9x = 123000-135000 -2x=-12000 -2x/-2=-12000/-2 x=6000 Amount invested at 7% = x = 6000 Amount invested at 9% = 15000-x = 15000 - 6000 = 9000 Check ===== 6000 * 7/100 + 9000 * 9/100 = 1230 60*7 + 90*9 = 1230 420 + 810 = 1230 1230=1230
 Money_Word_Problems/520138: A student takes out two loans, one at 5% interest and the other at 6% interest. The 5% loan is \$1000 more than the 6% loan, and the total interest for 1 year is \$215. How much is each loan?1 solutions Answer 345931 by Maths68(1474)   on 2011-10-24 11:49:10 (Show Source): You can put this solution on YOUR website! Let Loan taken on 6% = x Loan taken on 5% = x + 1000 Given Total interest = 215 x*6% + (x+1000)*5% = 215 x*(6/100) + (x+1000)*(5/100) = 215 Multiply by 100 both sides x*6 + (x+1000)*5=215*100 6x+5x+5000=21500 11x=21500 - 5000 11x=16500 11x/11=16500/11 x=1500 Loan taken on 6% = x = \$1500 Loan taken on 5% = x + 1000 = 1500+1000 = \$2500 Check ===== 1500 * 6/100 + 2500 * 5/100 = 215 15*6+25*5 = 215 90+125=215 215=215
 Linear-equations/520112: 1. What is the slope of the line passing through the points (2, 7) and (–1, 3)?1 solutions Answer 345928 by Maths68(1474)   on 2011-10-24 10:53:24 (Show Source): You can put this solution on YOUR website! points (2, 7) and (–1, 3) Slope of line = Rise in y / Rise in x m = (y2-y1)/(x2-x1) m=3-7/-1-2 m=-4/-3 m=4/3 Slope is 4/3
 Geometry_Word_Problems/520103: A rectangular window has a length that is three times the width, the perimeter is 56 feet, find the length and width of the window1 solutions Answer 345927 by Maths68(1474)   on 2011-10-24 10:50:38 (Show Source): You can put this solution on YOUR website!Perimeter = P = 56 Length = l = 3w (Given) Length = ? Width = ? Perimeter of rectangel = 2l + 2w p = 2l + 2w 56 = 2(3w) + 2w 56 = 6w + 2w 56 = 8w 56/8=8w/8 7=w w=7 Given Length = l = 3w Length = l = 3(7) Length = 21 Perimeter = P = 56 ft. Length = l = 21 ft. Width = 7 ft
 Complex_Numbers/520018: The attendance at a moving picture theater on a certain day was 737 persons. If there were 289 more adults than children, how children were there?1 solutions Answer 345914 by Maths68(1474)   on 2011-10-24 05:09:15 (Show Source): You can put this solution on YOUR website!Let Number of Children = x Number of Adults = x + 289 Adults + Children = 737 (x+289)+x=737 x+289+x=737 2x=737-289 2x=448 2x/2=448/2 x=224 Number of Children = x = 224 Number of Adults = x + 289 = 224+289=513 Check ====== Total Attendance = Adults + Children 737 = 513+224 737=737
 Quadratic_Equations/520027: Determine the quadratic equation whose solutions are: 3 and -2 1 solutions Answer 345913 by Maths68(1474)   on 2011-10-24 04:57:55 (Show Source): You can put this solution on YOUR website!Solution set = 3, -2 x= 3, or -2 x=3 or x=-2 x-3=0 or x+2=0 Since either of above is equal to zero, therefore multiplicatoin of the both will equal to zero (x-3)(x+2)=0 x^2+2x-3x-6=0 x^2-x-6=0 Required Quadratic Equation.
 Rectangles/519387: The area of a square rug in a library is 9 square feet. What is the perimeter of the rug?1 solutions Answer 345904 by Maths68(1474)   on 2011-10-24 02:18:41 (Show Source): You can put this solution on YOUR website!Area of Square = side * side Perimeter of Square = 4 * Side Given Area of Square = 9 sq ft. side * side = 9 (side)^2=9 Take sqour root both sides sqrt(side)^2=sqrt(9) side=sqrt(3*3) side=3 ft. Perimeter of Square = 4 * Side Perimeter of Square = 4 * 3 Perimeter of Square = 12 feet
 Rectangles/519948: A garden is shaped like a rectangle whose perimeter is 88 ft. The length is 10 ft more than the width. Find the length and width.1 solutions Answer 345903 by Maths68(1474)   on 2011-10-24 02:11:51 (Show Source): You can put this solution on YOUR website!A garden is shaped like a rectangle whose perimeter is 88 ft. The length is 10 ft more than the width. Find the length and width. P = 88 feet L = W + 10 W = ? L = ? Perimeter of regtangle = 2 length + 2 width P=2L + 2W 88 = 2 (W+10)+ 2W 88 = 2W+20+ 2W 88-20=4W 68=4W 68/4=W 17=W W=17 Given L=W+10 = 17+10 = 27 feet Perimeter = 88 feet Length = 27 feet Width = 17 feet
 Average/520008: if the average of 5 and k is equal to the average of 2,6 and k what is k value1 solutions Answer 345901 by Maths68(1474)   on 2011-10-24 01:57:52 (Show Source): You can put this solution on YOUR website!(5+k) / 2 = (2 + 6 + k)/3 (5+k) / 2 = (8 + k)/3 3(5+k)=2(8+k) 15+3k=16+2k 3k-2k=16-15 k=1 Check ====== (5+k) / 2 = (2 + 6 + k)/3 (5+1) / 2 = (2 + 6 + 1)/3 6/2=9/3 3=3
 Average/519932: Joe has scores of 94, 71, 89, 73 on his first four exams in his math class. He wants to get a final grade of B for the course. To do this, his exam average must be greater than or equal to 80 and less than 90. he has one exam remaining. What range of scores will give him a final grade of B Show the answer mathematically. Write the answer as a statement.1 solutions Answer 345899 by Maths68(1474)   on 2011-10-24 01:51:33 (Show Source): You can put this solution on YOUR website!Let Socre of fifth exam = x Avarage for five exams = (97+71+89+73+x)/5 = (324+x)/5 His exam average must be greater than or equal to 80 and less than 90 80≤(324+x)/5<90 Now For 80≤(324+x)/5 80≤(324+x)/5 Multiply by 5 5*80≤5*(324+x)/5 400≤(324+x) 400-324≤x 76≤x For (324+x)/5<90 Multiply by 5 5*(324+x)/5<90*5 324+x<450 x<450-324 x<126 Range of x 76≤x<126 Range of marks is between 76 and 125 He must score marks between 76 and 125 in his fifth test to maintain an average which will give him a grade B. If the total marks of an exam is 100 then range must be between 76 and 100.
 Travel_Word_Problems/519942: If I rode my bike 24 mile is 70 minutes, how many miles was I riding per hour?1 solutions Answer 345897 by Maths68(1474)   on 2011-10-24 00:55:39 (Show Source): You can put this solution on YOUR website!Change the minutes into hour 70 minutes = 70 * (1/60) hours 70 minutes = 7/6 hours 70 minutes = 1.17 hours Speed = Distance / time = 24/1.17 = 20.51 mph
 Money_Word_Problems/519963: ralph chase plans to sell a piece of property for \$180,000. He wants the money to be paid off in two ways- a short term note at 9% interest and a long term at 7% interest. find the amount of each note if the total annual interest paid is \$14,600. 1 solutions Answer 345896 by Maths68(1474)   on 2011-10-24 00:47:03 (Show Source): You can put this solution on YOUR website! Total Amount = \$180,000 Total Interest = \$14,600 Amount to be paid off at 9% = x Amount to be paid off at 7% = 180,000 - x Amount to be paid off at 9% * 9% + Amount to be paid off at 7% * 7% = Total Interest x*9/100 + (180000-x)*7/100=14600 x*0.09+(180000-x)*0.07=14600 0.09x+12600-0.07x=14600 0.02x=14600-12600 0.02x=2000 x=2000/0.02 x=100,000 Amount to be paid off at 9% = x = \$100,000 Amount to be paid off at 7% = 180,000 - 100,000 = \$80,000 Check ====== 100000 * 0.09 + 80000 * 0.07 = 14600 9000+5600=14600 14600=14600