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# Recent problems solved by 'monika_p'

 Miscellaneous_Word_Problems/472776: Bob Brown bought two plots of land for a total of \$110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was \$9600. How much did he pay for each piece of land? How do I start this one? I came up with .16x-.04y=\$110,000 .16x-.04y+.04y=\$110,000+.04y .16x=\$110,000+.04y 1/.016 .16x=\$110,000+.04y/ by 1/.16 Help figure where I went wrong? 1 solutions Answer 324132 by monika_p(71)   on 2011-07-21 11:03:40 (Show Source): You can put this solution on YOUR website!x-price of first plot y-price of second plot x+y=110,000 from first sentnce .16x-.04y=9600 from next sentences now solve as system of 2 equations x=110,000-y .16(110,000-y)-.04y=9600 17600-.16y-.04y=9600 -0.2y=-8000 y=40,000 then x=110,000-40,000=70,000
 Functions/472768: Factorize the binomial -1+y^2= ( ) ( ) Please explain the steps. 1 solutions Answer 324119 by monika_p(71)   on 2011-07-21 10:14:27 (Show Source): You can put this solution on YOUR website!This is example of difference of two squares Steps to solve it: find the square roots of the perfect squares, then one factor is their SUM (a+b) and the other factor is the DIFFERENCE between them (a-b) then
 Age_Word_Problems/472763: Igi is now twice as old as Bill. Seven years ago, the sum of their ages was 16. How old are they now?1 solutions Answer 324108 by monika_p(71)   on 2011-07-21 09:55:45 (Show Source): You can put this solution on YOUR website!x- Igi's age y-Bill's age x=2y info from the first sentence (x-7)+(y-7)=16 from the second sentence substitute for x (2y-7)+(y-7)=16 3y-14=16 3y=30 y=10 then x=20
 Travel_Word_Problems/472741: Plane A leaves airport 1 and heads for airport 2 which is a distance of 2,700 km. At the same time, plane B leaves airport 2 and heads for airport 1. Due to headwinds and tailwinds, Plane A's average speed is 100 kph greater than that of plane B. If the two planes pass each other after 3 hours, find the speed of each plane.1 solutions Answer 324106 by monika_p(71)   on 2011-07-21 09:49:18 (Show Source): You can put this solution on YOUR website!The first thing that you should understand here is that if the planes start at the same time then at the point at which they meet, the time will be the same t=3hr. In addition, the total distance travelled by the two planes will be equal to the sum of their individual distances travelled x+y=2700 speed of plane A Va=Vb+100kph the plane travelled 2700-y distance in t=3 hr speed of plane B is Vb the plane travelled 2700-x distance in t=3 hr using formula of the speed for the plane A we write for the plane B Now compare two equations Vb=Vb multiply both sides by 3 2y=2400 y=1200 then x= 1500 having the distance x and y the planes travelled in t=3hr you can find speed of each plane Va= x/t= 1500/3=500 kph Vb=y/t=1200/3=400kph
 Mixture_Word_Problems/472734: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?1 solutions Answer 324077 by monika_p(71)   on 2011-07-21 07:48:17 (Show Source): You can put this solution on YOUR website!x- liters of 20% alc. solution (x+40) - total liters of 30% solution x*20%+40*50%=(x+40)*30% 0.2x+40*0.5=(x+40)*0.3 0.2x+20=0.3x+12 0.1x=8 x=80 You have to add 80 liters of 20% alc. solution
 Travel_Word_Problems/472725: 1.) Jonathan drove his car from A to B at 81 km/hr. His car broke down and he returned by bus at 54 km/hr. his total travel was 5 hours. how long was his trip by car?1 solutions Answer 324071 by monika_p(71)   on 2011-07-21 07:19:29 (Show Source): You can put this solution on YOUR website!The speed formula is: v=d/t You have given speed from A to B v1=81km/hr speed from B to A v2=54km/hr total travel time t1+t2=5hr the distance d from A to B and B to A is the same Then v1=d/t1 d=v1*t1 v2=d/t2 d=v2*t2 since distnce is same you compare 2 equations v1*t1=v2*t2 81*t1=54*t2 Now use information about the time t1+t2=5hr ---> t1=5-t2 substitute and solve fo t2 81*(5-t2)=54*t2 405-81t2=54*t2 135*t2=405 t2=3hr then trip by car t1=2hr
 Age_Word_Problems/472729: Half of henry's age added to 1/3 of Daisy's age is 11 years. Six years from now, the sum of their ages will be 40 years. How old is each?1 solutions Answer 324065 by monika_p(71)   on 2011-07-21 06:29:49 (Show Source): You can put this solution on YOUR website!a-Henry's age b-Daisy's age From information you have you can write 2 equations 1/2a+1/3b=11 (a+6)+(b+6)=40 Solve it as system of 2 equations from second equation find a a=40-12-b a= 28-b put it in first equation and find b 1/2(28-b)+1/3b=11 14-1/2b+1/3b=11 -3/6b+2/6b=-3 -1/6b=-3 b=18 then a= 28-18=10
 Human-and-algebraic-language/472499: A new cruise ship has just launched 3 new ships; the Pacific Paradise, the Carribbean Paradise, and the Mediterranean Paradise. The Caribbean Paradise has 29 more rooms than the Pacific Paradise. The Meditteranean Paradise has 40 fewer rooms than three time the number of rooms on the Pacific Paradise. Find the number of rooms for each ship if the total number of rooms for the three ships is 534.1 solutions Answer 323959 by monika_p(71)   on 2011-07-20 17:52:01 (Show Source): You can put this solution on YOUR website!a- number of room on Pacific Paradise b-number of rooms on Carribbean Paradise c- number of rooms on Mediterranean Paradise given b=a+29 c=3a-40 a+b+c=534 then a+a+29+3a-40=534 a= 109 b=138 c=287
 Points-lines-and-rays/472513: The perimeter of a rectangle is 310 feet. The length is 25 feet more than the width. Find the width and the length of the rectangle and the corresponding area of the rectangle1 solutions Answer 323957 by monika_p(71)   on 2011-07-20 17:25:20 (Show Source): You can put this solution on YOUR website!a - lenght b- widht Given P=310 a= b+25 perimeter formula of rectangle P=2a+2b substitute for P and a 310=2*(b+25)+2b b=65 then a= 90 Now you can find area using formula A=a*b
 Travel_Word_Problems/472497: Driving at 51 MpH, one covers 19 miles in how many seconds? 1 solutions Answer 323952 by monika_p(71)   on 2011-07-20 17:12:09 (Show Source): You can put this solution on YOUR website!Given d= 19M v=51MpH As you have to find time in seconds and speed v is given in hr convert units knowing that 1hr= 3600s v== 0,0142 Mps speed formula v=d/t where v - speed, d-distance, t - time You have to find time, then t= d/v subsitute for d and v
 Quadratic_Equations/472475: The number of tickects sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+12x+11, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day? ^means raising to that power1 solutions Answer 323943 by monika_p(71)   on 2011-07-20 16:24:46 (Show Source): You can put this solution on YOUR website!In this case vertex is the high point of the parabola (ticket sales peak) because coefficient a= -0.4 is a negative number and the parabola opens downward To answer this question you have to find coordinates of the vertex of parabola N(x)= -0.4x^2+12x+11 where x is number of days and y = N(x) is number of tickets sold The general form of quadratic equation is y= ax^2+bx+c x-coordinate of vertex y-coordinate of vertex where d= b^2-4*a*c Substitute for a, b, and c and you should get answer that on 15th day x=15 they will sell the most tickets y=101
 Polynomials-and-rational-expressions/472466: I am in college prep math and had a question about multiplying and simplifying rational expressions. The problem I am stuck on is xsquared-25 over xsquared-3x-10 times or multiplied by x+2 over x I factored the numerator and denominator then cancelled out similar factors The answers I got were x+5 over x which I simplified to 5 by canceling out the x's1 solutions Answer 323933 by monika_p(71)   on 2011-07-20 15:36:28 (Show Source): You can put this solution on YOUR website!You got the right answer You can not simplify by canceling out the x when there is "+ " but you can write it as a sum of two fractions
 Rectangles/470578: Respected Sir, The length and breadth of a rectangle are in the ration 8:5. The length is 10.5 centimeters more than the breadth. What are the length and breadth of the rectangle. Kindly explain steps too. Rgds/Sunil1 solutions Answer 322885 by monika_p(71)   on 2011-07-15 16:18:31 (Show Source): You can put this solution on YOUR website!The ratio we can write as: l/b=8/5 it is given that lenght is 10.5 cm more than breadth then l=b+10.5, now substitute for l 8b=5(b+10.5) 3b=52.5 b=17.5 then l=b+10.5=17.5+10.5=28
 Percentage-and-ratio-word-problems/470634: the ratio of two numbers is 42 to 9. Also, four times the larger number is 8 greater than 16 times the smaller number. what are the numbers?1 solutions Answer 322874 by monika_p(71)   on 2011-07-15 16:00:42 (Show Source): You can put this solution on YOUR website!a larger number b smaller number From the first sentence we have ratio a/b=42/9 9a=42b From second sentence we know that if we multiply b by 16 and add 8 to that number we will get 4a 4*a=16*b+8 a=4*b+2 Now we can substitute for a 9( 4b+2)=42b 36b+18=42b 6b=18 b=3 then for b=3 a =4*3+2=14
 Travel_Word_Problems/470628: The airplane could fly 2080 miles in 5 more hours than it took the sports car to drive 195 miles. The speed of the airplane was 4 times the speed of the sports car. Find the speeds and times of both1 solutions Answer 322865 by monika_p(71)   on 2011-07-15 15:25:21 (Show Source): You can put this solution on YOUR website!for the airplane d=2080, t=t1+5, and v=4*v1 for the car d1=195, t1=? , and v1=? speed formula for the airplane we can write: for the car since the first equation for airplane has 2 unknown lets substitute v1 from 2nd equation 1300t1=3900 t1=3 then t=t1+5 = 8 v=4*v1=4*65=260
 Expressions-with-variables/470667: 7/6p^2+q / 14/18p^2+3q1 solutions Answer 322855 by monika_p(71)   on 2011-07-15 14:09:21 (Show Source): You can put this solution on YOUR website!(7/(6p^2*q))/(14/(18p^2*3q)) use the formula of dividing two fractions = then: = =
 Functions/235230: you join an aerobics class at a local gym. the cost is \$3 per class plus \$10 for the initial membership fee. write an equation that shows the relationship between the number of classes n you attend and the amount you pay p. i am in 8th grade and do not understand how to do this problem and my mom is smart and usually helps me but even she is stumped on this one. i hope you can help. thank you in advance for your help.1 solutions Answer 173330 by monika_p(71)   on 2009-11-04 19:38:59 (Show Source): You can put this solution on YOUR website!p - amount you pay n- number of classes \$10 - membership fee \$3 cost of one class multiply number of attended classes by cost of one class and add 10 because you pay it only once Then: p=3n+10
 absolute-value/234370: I am starting college again and this is a practice question on a review and I can't even remember where to begin with this. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? It does have multiple choice and they are. A. 2 hours and 24 minutes B. 3 hours and 12 minutes C. 3 hours and 44 minutes D. 4 hours and 10 minutes E. 4 hours and 33 minutes Thank you for your help. I haven't don't algebra in 10 years or longer. I have always done well and I think with the a little refreshing I will do better.1 solutions Answer 172815 by monika_p(71)   on 2009-11-02 21:04:09 (Show Source): You can put this solution on YOUR website! Sally can paint a house in 4 hrs so her rate is 1/4 (1/4 of the house will be painted in one hr), and Joh can paint house in 6 hrs , his rate is 1/6 In x hours, Sally paints x/4 of the room and John paints x/6 of the room. Since they will be working together, we will add the two parts together. The sum equals one complete job and gives us the following equation: solving for x: 3x/12+2x/12=1 5x/12=1 5x=12 x=12/5 x=2 2/5 2hr 24mins
 Trigonometry-basics/234320: please help solve: (cot(x)/csc(x)+1)=(csc(x)-1/cot(x))1 solutions Answer 172803 by monika_p(71)   on 2009-11-02 20:22:37 (Show Source): You can put this solution on YOUR website! cross multiply : use formula : substitute csc(x)= 1/sin(x) cot(x)=cos(x)/sin(x): multiply both sides by sin^2(x) <---- Pythagorean trigonometric identity
 Quadratic_Equations/179152: Pleae help. Find all real and imaginary solutions to each equation. b^4+13b^2+36=01 solutions Answer 134377 by monika_p(71)   on 2009-01-31 00:09:48 (Show Source): You can put this solution on YOUR website!b^4+13b^2+36=0 substitute b^2=t t^2+13t+36=0 discriminant: b^2-4ac=13^2-4*1*36=25 t1=-13-sqrt(25)/2*1 t1=-9 t2=-13+sqrt(25)/2*1 t2=-4 Now we have to go back to substitution b^2=t and substitute t1 and t2 in the place of t for b^2=-9 b=sqrt(-9) b1=sqrt(9*-1)=sqrt(9*i^2) b1=3i for b^2=-4 b=sqrt(-4) b2=sqrt(4*-1)=sqrt(4*i^2) b2=2i answer: b1=3i b2=2i
 expressions/179143: a-2b/a+2b = 1k+1 solve for a: 1 solutions Answer 134375 by monika_p(71)   on 2009-01-30 23:27:11 (Show Source): You can put this solution on YOUR website!a-2b/a+2b = 1k+1 multiply both sides by (a+2b) a-2b=(k+1)(a+2b) multiply two () on the right side a-2b=ak+2bk+a+2b shift terms with a on the left side and all rest on the left a-ak-a=2bk+2b+2b -ak=2bk+4b divide both sides by -k a=-2b(k+2)/k
 Exponents-negative-and-fractional/179145: Id be more than greatful if someone could help me with these two problems; (I should just solve and check) but they are never equal when I solve them. x-12=-8(x-3) x^2-3x+5= x(x-8)+201 solutions Answer 134374 by monika_p(71)   on 2009-01-30 23:00:44 (Show Source): You can put this solution on YOUR website!x-12=-8(x-3) x-12=-8x+24 add 8x to both sides x+8x-12=-8x+8x+24 9x-12=24 add 12 9x-12+12=24+12 9x=36 divide both sides by 9 x=4 Check: 4-12=-8(4-3) -8=-8 ----------------------- x^2-3x+5= x(x-8)+20 x^2-3x+5=x^2-8x+20 subtract x^2 from both sides x^2-x^2-3x+5=x^2-x^2-8x+20 -3x+5=-8x+20 add 8x to both sides -3x+8x+5=-8x+8x+20 5x+5=20 subtract 5 5x+5-5=20-5 5x=15 divide by 5 x=3 Check: 3^2-3*3+5=3(3-8)+20 9-9+5=-15+20 5=5
 Polygons/179269: find the length of the secon base of a trapezoid with area 14 units height 4 units and base 4.5 units? Find the height of a triangle with are 12 square units and base 3 units? find the perimeter of an equilateral rectangle with area 1/16 square units? Find the area of a circle with circumference 8 pi units?1 solutions Answer 134326 by monika_p(71)   on 2009-01-30 17:57:48 (Show Source): You can put this solution on YOUR website!1.find the length of the second base (a) of a trapezoid with area A=14 units height h=4 units and base b=4.5 units? multiply both sides by 2/h subtract b substitute for A, h, and b a=2.5 2.Find the height (h) of a triangle with area A= 12 square units and base a=3 units? A=1/2*a*h multiply both sides by 2/a h=2A/a h=2*12/3 h=8 3.find the perimeter (P) of an equilateral rectangle with area A=1/16 square units? Equilateral means that all the sides are equal. Therefore, an equilateral rectangle is a square. A=a^2 a=sqrtA a=sqrt(1/16) a=1/4 P=4a P=4*1/4 P=1 4.Find the area (A)of a circle with circumference c=8 pi units? c=d*pi d=c/pi d=8*pi/pi d=8 diameter, d=2r, r-radius A=pi*r^2=1/4*pi*d^2 A=1/4*pi*8^2 A=16*pi
 Graphs/179380: Solve the inequality -2-4m-m<7m-2 1 solutions Answer 134313 by monika_p(71)   on 2009-01-30 17:00:51 (Show Source): You can put this solution on YOUR website!-2-4m-m<7m-2 -2-5m<7m-2 add 5m to both sides -2-5m+5m<7m+5m-2 -2<12m-2 add2 to both sides -2+2<12m-2+2 0<12m divide by 12 m >0
 Equations/179038: This question is from textbook glencoe mathematics c-5d=2 2c+d=41 solutions Answer 134017 by monika_p(71)   on 2009-01-28 19:26:04 (Show Source): You can put this solution on YOUR website!c-5d=2 / multiply by -2 2c+d=4 -2c+10d=-4 2c+d=4 --------- add two equations 11d=0 d=0 then from first equation: c=2-5d substitute for d=0 c=2-5*0 c=2 Answer: c=2 d=0
 Travel_Word_Problems/176536: It take Felicia 25 minutes to walk one mile. At this rate, how long would it take her to walk 7 miles? I multiplied 25 x 7 = 175 minutes. But am confused trying to use the formula. D=RT D=7 miles, R=25 min/mile, T=T 7=25T 7/25 = T T= .28 minutes What am I not understanding? Thanks for your help!1 solutions Answer 131632 by monika_p(71)   on 2009-01-13 22:04:09 (Show Source): You can put this solution on YOUR website!rate unit is mile/min (R=D/T) in this case you have R=1mile/25min =0.04 mile/min having R you can find time Felicia needs to walk 7miles D=R*T T=D/T=7/0.04=175min
 Numbers_Word_Problems/175343: if 25 is added to three times of a number 52 is obtained. find the number.1 solutions Answer 130514 by monika_p(71)   on 2009-01-07 15:07:38 (Show Source): You can put this solution on YOUR website!x- unknown number 25+3x=52 3x=27 x=9 <--answer
 Numbers_Word_Problems/175346: a number is twice another number. if their sum is 48 find the numbers. 1 solutions Answer 130511 by monika_p(71)   on 2009-01-07 15:02:26 (Show Source): You can put this solution on YOUR website!x-first number y- second number x=2y x+y=48 solve as system of two equations : 2y+y=48 3y=48 y=16 then x=32
 Rectangles/175364: 25: The length of a rectangle is three times its width. If the perimeter of the rectangle is 48, what is its area?1 solutions Answer 130423 by monika_p(71)   on 2009-01-07 10:05:44 (Show Source): You can put this solution on YOUR website!x-widht y=3x-lenght P=48 Perimeter formula: P=2*widht+2*lenght Area formula: A=widht*lenght Find x from perimeter formula: 48=2*x+2*3x 48=8x x=6 widht then lenght y=18 Now find A A=6*18=108
 Expressions-with-variables/175233: i cant figure out how to get "X" and "Y"... 4x + 6y = 38 10x + 8Y = 60 they have steps but i dont understand them, please help1 solutions Answer 130310 by monika_p(71)   on 2009-01-06 15:00:40 (Show Source): You can put this solution on YOUR website!one of the method to solve system of equation is method of elimination. 4x+6y=38 10x+8y=60 lets eliminate x, to do so you have to multiply both equations first by 10 and second by -4 then you will get 40x+60y=380 -40x-32y=-240 as you see you got 40x in first equation and -40x in second - opposits, after adding first equation to the second x will be eliminated: 40x-40x+60y-32y=380-240 28y=140 / divide both sides by 28 y=5 to find x substitute y=5 in either first or second equation 4x+6*5=38 4x+30=38 4x=8 x=2 If you want eliminate y you will get same results: 4x+6y=38/*8 10x+8y=60/*-6 32x+48y=304 -60x-48y=-360 ------------------ -28x=-56 / divide by -28 x=2 then 10*2+8y=60 8y=60-20 8y=40 y=5
 Linear-systems/175230: Please solve x + 1 = 2/3x algrbracially. Please, step by step, I need to see how the answer is -3. Cannot figure this out.1 solutions Answer 130305 by monika_p(71)   on 2009-01-06 14:35:38 (Show Source): You can put this solution on YOUR website!To solve this equation group all x on one side and rest on the other side of = sign. Remember that whatever you do to left side of the equation the same you have to do to the right, and opposit. x+1=2/3x subtract 2/3x from both sides so you will not have any x on the right side x-2/3x-1=2/3x-2/3x x-2/3x-1=0 add 1 to both sides to remove number from rigt side (we want only x there) x-2/3x-1+1=-1 x-2/3x=-1 3/3x-2/3x=-1 1/3x=-1 /3 multiply by 3 to get just x on the left side x=-3