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# Recent problems solved by 'oberobic'

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 Coordinate-system/280564: Graph the equation and identify the y-intercept: 4y+5x= -12. The y-intercept is?1 solutions Answer 203944 by oberobic(2304)   on 2010-03-14 12:45:21 (Show Source): You can put this solution on YOUR website!First, get the equation into slope-intercept form: y = mx + b 4y + 5x = -12 subtract 5x from both sides 4y = -5x -12 divide both sides by 4 y = -5/4x -12/3 y = -5/4x -4 . Recall, the x-intercept is the point where y=0 and the y-intercept is the point where x=0. Thinking visually, the point (0, ??) will be on y-axis somewhere; likewise the point (??, 0) will be on the x-axis somewhere. Since we're drawing a line, it will cross at these points. . To find the y-intercept, simply set x=0: the y-intercept is -4, which is at the point (0,-4) . Thinking about the slope-intercept equation, we know the slope is the coefficient of x. In this case the slope is -5/4, which means it slopes downward from the upper left to the lower right. We can find the x-intercept by setting y=0 and working it out. 0 = -5/4x -4 adding 5/4x to both sides 5/4x = -4 multiply both sides by 4 5x = -16 divide both sides by 5 x = -16/5 so the x-intercept is (-16/5, 0) . Now you have two points: (0,-4) and (-16/5,0). With two points you can draw line. Plot the two points and graph the equation. . . A good check is to find another point and verify it is on the line. Say x= -4, which neatly cancels the denominator... y = -5/4(-4) -4 y = 20/4 -4 y = 5 -4 y = 1 . Is the point (-4,1) on the line? Yes, it is. . Done.
 Polynomials-and-rational-expressions/280570: The base of a triangle is 6cm greater than the height. The areas is 20cm^2 Find the height and length of the base height of triangle is ____ cm. base of triangle is ____ cm.1 solutions Answer 203941 by oberobic(2304)   on 2010-03-14 12:25:31 (Show Source): You can put this solution on YOUR website!Start with your variables... A = area of a triangle = 1/2*base*height h = height of the triangle b = base of the triangle b = h + 6 :: the base is 6 cm > height A = 20 cm^2 . Substitute what we know... 20 cm^2 = 1/2*b*h 20 = 1/2(h+6)*h multiply both sides by 2 40 = (h+6)*h = h^2 + 6h subtract 40 from both sides 0 = h^2 + 6h - 40 so h^2 + 6h - 40 = 0 factor (h+10)(h-4) = 0 which means our solutions are h = -10 h = 4 of course negative height is nonsense which means h = 4 is the solution to test . substituting what we know about the base b = h+6 = 10 . checking the area 1/2*4*10 = 20? 2* 10 = 20 Yes. . Answer: The height of the triangle is 4 cm. The base of the triangle is 10 cm. . Done
 Equations/280340: 10a + 2b = 15 and 5a = 4b, what is the value of a + b?1 solutions Answer 203840 by oberobic(2304)   on 2010-03-13 19:02:40 (Show Source): You can put this solution on YOUR website!10a + 2b = 15 5a - 4b = 0 . Multiply 2nd equation by 2 and then subtract . 10a + 2b = 15 10a - 8b = 0 10b = 15 b = 1.5 . 5a = 4b 5a = 4*1.5 = 6 a = 1.2 . Checking...does 10a + 2b = 15? . 10a = 10*1.2= 12 2b= 2*1.5 = 3 12+3 = 15 Check. . Answer: a + b = 1.2+1.5 = 2.7 . Done.
 Linear_Equations_And_Systems_Word_Problems/279087: The scenario below can be represented by a system of equations. Show representations that can be used and respond to the questions. “Two small bottles and one large bottle can hold 10 cups of water. One large bottle minus one small bottle will give you 4 cups of water. How many cups of water can each bottle hold?” Thanks for your help in advance.1 solutions Answer 202976 by oberobic(2304)   on 2010-03-09 22:00:59 (Show Source): You can put this solution on YOUR website!L = volume of liquid held by a large bottle S = volume of liquid held by a small bottle 2S + L = 10 cups or L + 2S = 10 . L - S = 4 cups . L + 2S = 10 L - S = 4 . Subtracting the second equation from the first. 3S = 6 Divide both sides by 3 S = 2 . Looking back, we see L = S + 4 = 2 + 4 = 6 . Checking these values to see if they're correct... . L + 2S = 10?? 6 + 2*2 = 10?? Yes. . Answer: The volume of the large bottle is 6 cups. The volume of the small bottle is 2 cups.
 Systems-of-equations/279072: carmen can weed the garden in 24min. if kim helps they can finish in 8 min. how long would it take kim working alone?1 solutions Answer 202974 by oberobic(2304)   on 2010-03-09 21:51:52 (Show Source): You can put this solution on YOUR website!For jobs like this, look at it terms of the whole job being a unitary thing. Carmen can do the job in 24 minutes, so she does the job at a rate of 1/24 of the total job per minute. Carmen and Kim working together can do the job in 8 minutes, so their combined rate is 1/8 per minute. Algebraically, their combined speeds can be shown as: Multiplying through by 24x we have Subtracting x from both sides Dividing both sides by 2 Kim can do the job in 12 minutes working alone. . Checking our work, we were told that combined they did the job in 8 minutes. In 8 minutes, Carmen can do of the job. In 8 minutes, Kim can do of the job. 1/3 + 2/3 = 1 job. . Done
 Probability-and-statistics/279079: In a shipment of 50 calculaters,4 are defective.One calculater is randomly selected and tested. WHAT IS THE PROBABILITY IT IS NOT DEFECTIVE ? 1 solutions Answer 202970 by oberobic(2304)   on 2010-03-09 21:32:23 (Show Source): You can put this solution on YOUR website!There are 50 ways you can pick 1 item from a set of 50 items. We're told that 4 of the 50 are defective, so 4/50 are bad. So, picking 1 item, you would have a 4/50 or 1/12.5 or an 8% chance of drawing a bad one. OR You have a 46/50 chance of picking a good one, or 92%. That means the chance of drawing a bad one is 100% - 92% = 8%. . Done
 Graphs/279074: sketch the graph of the equation 5x+4y=201 solutions Answer 202968 by oberobic(2304)   on 2010-03-09 21:27:04 (Show Source): You can put this solution on YOUR website!First, get it in y = mx+b format so that you can graph it. 5x + 4y = 20 subtract 5x from both sides 4y = -5x + 20 divide both sides by 4 y = -5/4x + 5 . x = 0, y = 5 results in the point (0,5) x = 4, y = 0 results in the point (4,0) . with two points you can graph a straight line .
 Mixture_Word_Problems/279075: how much soap is needed to make 10 liters of a 20% soap solution1 solutions Answer 202966 by oberobic(2304)   on 2010-03-09 21:23:06 (Show Source): You can put this solution on YOUR website!Volume = 10 liters Desired solution is 20% soap, so we assume that 80% is pure water. Assuming we are measuring volumes, then the amount of pure soap in 10 liters of 20% soap is .2*10 = 2 liters of pure soap. That means we add 8 liters of pure water to arrive at 10 liters.
 Rectangles/279061: A rectangle's length is 3 times its width. Its area is 108 square cm. What are its dimensions.1 solutions Answer 202964 by oberobic(2304)   on 2010-03-09 21:20:38 (Show Source): You can put this solution on YOUR website! . . The square root of 36 is either +6 or -6, BUT a negative width does not make sense, so we can start with w=6. . . Checking the A OK. . Answer: The rectangle's length is 18; the width is 6. . Done
 Age_Word_Problems/279065: Anita has two sisters and three brothers. The mean of all their ages is 6 years. What will their mean age be 10 years from now? Twenty years from now?1 solutions Answer 202963 by oberobic(2304)   on 2010-03-09 21:10:05 (Show Source): You can put this solution on YOUR website!mean = sum / count mean = 6 count = 6 x = sum 6 = x / 6 x = 36 . In 10 years, the sum will be x+10 = 36 + 10 = 46 mean = 46 / 6 = 7 2/3 = 7.67 . Done
 Coordinate-system/277282: how do i do a problem like this -16x+2y=-6 through point (16,8)1 solutions Answer 201962 by oberobic(2304)   on 2010-03-04 21:51:54 (Show Source): You can put this solution on YOUR website!First, get the equation into slope-intercept form: y = mx+b -16x + 2y = -6 2y = 16x - 6 y = 8x - 3 . But this line does NOT go through the point (16,8), as we can see on a graph. In fact, y = 125 when x=16. . However, the general equation y = mx+b can be shifted with any constant 'b'. 8 = 8(16) + b 8 = 128 + b b = -120 We can graph this as follows. So the equation y = 8x - 120 will have slope = 8 and it will go through the point (16,8). . We can check this answer by remembering the slope = rise / run = change in y / change in x. The slope m = 8. So if we move one point on the x-axis, there will be a change of 8 on the y-axis. Given (16,8), we can predict that (15,0) will be on the line. (-1 on the x-axis leads to -8 on the y-axis) And we can predict (17,16) will be on the line. (+1 on the x-axis leads to +8 on the y-axis) Looking back at the second graph, we see that is the case.
 Mixture_Word_Problems/277315: one acetic acid solution is 70% water and another is 30% water. how many liters of each solution should be mixed to produce 20 liters of a solution that is 40% water?1 solutions Answer 201960 by oberobic(2304)   on 2010-03-04 21:14:42 (Show Source): You can put this solution on YOUR website!With 'solution' problems, you have to keep track of how much pure stuff you need. This question is tricky because the question presents the complementary percentages. Solution 1 is 70% water, so it is 30% pure acetic acid. We normally call that a 30% solution. Solution 2 is 30% water, so it is 70% pure acetic acid. We normally call that a 70% solution. The goal is 20 liters of a 60% acetic acid solution. . x = volume of 30% solution 20 - x = volume of 70% solution . .3x = amount of pure acetic acid .7(20-x) = the other amount of pure acetic acid. . 20 liters of 60% acetic acid will have .6*20 = 12 liters of pure acetic acid. . .3x + .7(20-x) = 12 . .3x + 14 - .7x = 12 -.4x = -2 x = -2/-.4 = 5 liters of 30% solution which means there is 15 liters of 70% solution. . checking to see if we have 12 L of pure acetic acid . .3*5 + .7*15 = 1.5 + 10.5 = 12 . So, 5 liters of 30% acetic acid + 15 liters of 70% acetic acid results in 20 liters of 60% acetic acid solution. . Reviewing the question, we need to give the complementary answer in terms of percentage of water. . Answer: 5 liters of 70% water + 15 liters of 30% water = 20 liters of 40% water
 Miscellaneous_Word_Problems/277314: five pens of the same type cost the same as two notebooks of the same type.If one pen and 2 notebooks cost\$4.20 how much does one one pen cost?1 solutions Answer 201956 by oberobic(2304)   on 2010-03-04 20:57:39 (Show Source): You can put this solution on YOUR website!5p = 2n, where p = cost of pens and n = cost of notebooks so, n = 2.5p . p + 2n = 4.20, which is given . substituting p + 2(2.5p) = 4.20 p + 5p = 4.20 6p = 4.20 p = .70 = 70 cents = cost of one pen . We also can calculate the cost of one notebook. 5p = 2n 5(.70) = 2n 3.50 = 2n n = 1.75 . Done
 Linear-equations/277322: 5x-10y=-5 -10x-10y=10 solve by the substitution1 solutions Answer 201948 by oberobic(2304)   on 2010-03-04 20:00:14 (Show Source): You can put this solution on YOUR website!5x -10y = -5 -10x -10y = 10 . subtract the second equation from the first . 15x = -15 x = -1 . substituting to find y . 5(-1) - 10y = -5 -5 -10y = -5 adding 5 to both sides -10y = 0 so... y = 0 . Answer: x = -1 y = 0 . Done
 Travel_Word_Problems/277320: a plane flew 800 miles in 4 hours while flying with the wind. against the wind, it took the plane 5 hours to travel 800 miles. find the rate of the plane in calm air and the rate of the wind.1 solutions Answer 201947 by oberobic(2304)   on 2010-03-04 19:55:56 (Show Source): You can put this solution on YOUR website!p = plane's speed in calm air w = wind's speed p + w = speed across the ground of the plane flying with the wind p - w = speed across the ground of the plane flying against the wind . d = rt is the standard distance equation, where d=distance, r=rate, t=time d = 800 miles is given . 800 = 4(p+w) :: given that it takes 4 hrs with the wind to travel 800 miles 800 = 5(p-w) :: given that it takes 5 hrs against the wind to travel 800 miles . so we have 4(p+w) = 800 5(p-w) = 800 . 4p + 4w = 800 5p - 5w = 800 . multiply the first equation by 5 and the second by 4 . 20p + 20w = 4000 20p - 20w = 3200 . add them . 40p = 7200 p = 180 . substituting for p = 180, we can find w . 4p + 4w = 800 divide by 4 p + w = 200 180 + w = 200 So, w = 20 . checking our work. . 4(180+20) = 800?? 4(200) = 800 Yes . 5(180-20) = 800?? 5(160) = 800 Yes. . Answer: Plane flies at 180 mph in calm air. Wind is blowing at 20 mph. . Done
 Surface-area/277321: the perimeter of an equilateral triangle is 10.5 cm. find the length of each side.1 solutions Answer 201940 by oberobic(2304)   on 2010-03-04 19:45:13 (Show Source): You can put this solution on YOUR website!With an equilateral triangle, all sides are equal, so a = b = c, where a = one side's length, b = another side's length, and c = final side's length. The perimeter of a triangle = a+b+c = 10.5 OR 3a = 10.5 a = 3.5 which means b = 3.5 and c = 3.5 . done
 Linear_Algebra/277305: I need help with this problem. The inner rectangle whose length is 7 inches and width is 13 inches is surrounded by a rectanglar frame whose uniform thickness is 2.5 inches. Find the area.1 solutions Answer 201939 by oberobic(2304)   on 2010-03-04 19:39:13 (Show Source): You can put this solution on YOUR website!Given the uniform width of the border is 2.5 inches, then you will need to add 5 inches to the inner rectangle's length and width to determine the outer rectangle's area: l + 5 = 7 + 5 = 12 w + 5 = 13 + 5 = 18 So, the outer rectangle's area = l*w = 12*18 = 216 . The inner rectangle's are = 7 * 13 = 91 . That means the area of the 'border' = 216 - 91 = 125 . Done
 Linear-equations/277310: how to show the graph of y=-4x thanks1 solutions Answer 201935 by oberobic(2304)   on 2010-03-04 19:28:09 (Show Source): You can put this solution on YOUR website!y = -4x . We know it is a straight line because there are no exponents. To draw a straight line, you only need two points. . So, pick a couple of values of 'x' and compute the values of 'y' for example... x = 2, y = -8 x = -2, y = 8 . The two point are thus: (2,-8), (-2, 8) Plot them and draw the line. .
 Miscellaneous_Word_Problems/277285: The sum of the digits of a two- digit number is 14. When the digits are reversed, the new number is 36 more than the original number. What is the original number?1 solutions Answer 201930 by oberobic(2304)   on 2010-03-04 19:20:45 (Show Source): You can put this solution on YOUR website!When solving number problems like these, we have to keep in mind the place values. For example, the number 23 actually means 2*10 + 3*1. Since the numbers are unknown in this word problem, we can call them 'xy'. BUT keep in mind that they are just standing next to each other, they're not being multiplied. The value would be 10x + y. . We are told some characteristics of the number 'xy'... x + y = 14 . That's easy, but the second statement is harder to set up. . Remember, the VALUE of 'xy' is 10x + y. So, reversing the digits to be 'yx' would change the VALUE to 10y + x. . We're told 10y + x is 36 more than 10x + y, which algebraically is 10y+x = 10x+y+36 . Rearranging this equation we have: x + 10y = 10x + y + 36 x -10x + 10y - y = 36 -9x + 9y = 36 dividing by 9 -x + y = 4 . Now we have to the two equations x + y = 14 -x + y = 4 . Adding we obtain 2y = 18 y = 9 . Since x+y = 14, then x = 14-9 = 5 . Checking... xy = 59 . yx = 95 . Is 95 = 59 + 36?? Yes. . Answer: The original number was 59. . Done
 Volume/277301: waht would be the height of a cylinder if the volume is 91in. and has a radius of 4in.1 solutions Answer 201926 by oberobic(2304)   on 2010-03-04 19:11:51 (Show Source): You can put this solution on YOUR website!volume of a cylinder = area of base * height = pi*r^2 * height . we are told volume = 91 and r=4 . 91 = pi(4^2) * h 91 = pi(16) * h 91 = 16pi * h . dividing by 16*pi . 91/(16*pi) = h . so the height is about 17.8678 in. . done
 Rectangles/277296: The area of a rectangle is 32 square inches. The length is 4 inches longer than the width. What is the length? What is the width? What is the perimeter?1 solutions Answer 201924 by oberobic(2304)   on 2010-03-04 19:05:48 (Show Source): You can put this solution on YOUR website!The area of a rectangle = length * width = l * w = 32 sq inches . l = w + 4 :: given . substituting (w+4) * w = 32 w^2 + 4w = 32 w^2 + 4w - 32 = 0 . factoring (w+8)(w-4) = 0 . so the solutions are w=-8 and w=4. of course, a negative length is nonsense, so the only answer appears to be w=4 . given l = w+4, then l= 4+4 = 8 . checking the area 4*8 = 32?? yes . the perimeter of a rectangle = 2l + 2w = 2(8) + 2(4) = 16+8 = 24 . Answer: Length = 8 Width = 4 Perimeter = 24 . done
 Travel_Word_Problems/277289: A car rental company has two rental rates. Rate 1 is \$63 per day plus \$0.18 per mile. Rate 2 is \$126 per day plus \$0.09 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking Rate 2?1 solutions Answer 201921 by oberobic(2304)   on 2010-03-04 18:56:50 (Show Source): You can put this solution on YOUR website!y = mx + b is the standard slope-intercept formula for a line we can put the information given into two equations in slope-intercept format R1 = .18x + 63, where x= miles driven R2 = .09x + 126 . we can graph the two lines to see where they cross R1 = red line, which has a steeper slope R2 = green line, which has a lower slope . . it appears the lines cross at about x=700 (or 700 miles driven) . of course, we know R1 and R2 really are just other names for 'y' . y = .18x + 63 y = .09x + 126 . multiplying both equations by 100 to remove decimals 100y = 18x + 6300 100y = 9x + 12600 . rearranging to put into simultaneous equation format . -18x + 100y = 6300 -9x + 100y = 12600 , subtracting the second equation from the first -9x = -6300 . dividing both sides by -9 x = 700 . so we confirm that the two lines cross at x=700. . that means that at a distance driven 'x' of 700, the cost of the two rental plans is the same. . but after that point, the line with lower slope rises more slowly, which means the other plan (the one with the steeper slope) is more expensive and getting more expensive for every mile driven > 700. . Answer: You need to drive more than 700 miles for Rate 2 to be less expensive than Rate 1. .
 Rate-of-work-word-problems/277280: It takes Cathy 1.5 hours to paddle her canoe 6 miles upstream. Then she turns her canoe around and paddles 6 miles downstream in 1 hour. What is the rate of the current? What is Cathy's paddling rate in still water?1 solutions Answer 201909 by oberobic(2304)   on 2010-03-04 18:36:18 (Show Source): You can put this solution on YOUR website!p = paddling rate in still water c = current flow p-c = speed going upstream p+c = speed going downstream d = rt, where d=distance, r=rate (or speed), and t= time . 1.5*(p-c) = 6 miles = distance upstream 1*(p+c) = 6 miles = distance downstream . multiplying through . 1.5p - 1.5c = 6 p + c = 6 . dividing the first equation by 1.5 p - c = 4 . solving as simultaneous equation, we can add them p + c = 6 p - c = 4 2p = 10 p = 5 = paddling rate . substituting this value p + c = 6 5 + c = 6 c = 1 . checking by substituting in the other equation . 1.5(p-c) = 6 ?? 1.5(5-1) = 1.5*4 = 6 yes . so the answer is: The rate of the current is 1 mph. Cathy's paddling rate in still water is 5 mph. . done
 Age_Word_Problems/276438: Two Questions : Cody is Twice as old as Evan. Three years ago the sum of their ages was 27. Find the age of each boy. Jack is twice as old as Lacy. In Three years the sum of their age will be 54. How old are they now. Your help is greatly appreciated :D1 solutions Answer 201450 by oberobic(2304)   on 2010-03-02 23:31:22 (Show Source): You can put this solution on YOUR website!C = Cody's age E = Evan's age C = 2E :: Cody is twice as old as Evan. Three years ago can be shown as: C -3 = Cody's age 3 years ago E -3 = Evan's age 3 years ago C-3 + E-3 = 27 :: Given C + E = 33 Substituting C = 2E 2E + E = 33 3E = 33 E = 11 Therefore C = 2E = 22 How old were they 3 years ago? C-3 = 19 E-3 = 8 Was the sum of their ages 27 back then? 19 + 8 = 27 ?? Yes. Answer: Cody's age is 22. Evan's age is 11. . J = Jack's age L = Lacy's age J = 2L In three years, their ages will be: J+3 and L+3 Then the sum will be 54. J+3 + L+3 = 54 J + L = 48 Substitue J = 2L 2L + L = 48 3L = 48 L = 16 J = 2L = 2(16) = 32 How old will they be in 3 years? J = 35 L = 19 Will the sum of their ages be 54 then? 35 + 19 = 54 ?? Yes. Answer: Jack's age is 32 and Lacy's age is 16. . Done
 Money_Word_Problems/276428: Kate bought 3 used CDs and 1 used DVD at the bookstore. Her friend Joel bought 2 used CDs and 2 used DVDs at the same store. If Kate spent \$20 and joel spent \$22, determine the cost of the used CD and the used DVD1 solutions Answer 201449 by oberobic(2304)   on 2010-03-02 23:22:14 (Show Source): You can put this solution on YOUR website!C = number of CDs D = number of DVDs . Kate bought 3 CDs and 1 DVDs for \$20: 3C + D = 20 . Joel bought 2 CDs and 2 DVDs for \$22: 2C + 2D = 22 . Two equations and two unknowns can be solved using simultaneous equations. . 3C + D = 20 2C + 2D = 22 . Multiply the first equation by 2 and then subtract the second equation: 6C + 2D = 40 2C + 2D = 22 4C = 18 C = 4.50 . Substituting to find D: 2C + 2D = 22 2(4.5) + 2D = 22 2D = 13 D = 6.50 . Checking 3C + D = 20 ?? 3(4.50) + 6.50 = 13.50 + 6.50 = 20 Yes. . Double checking... 2C + 2D = 22 ?? 2(4.50) + 2(6.50) = 9 + 13 = 22 Yes. . Answer: Used CDs cost \$4.50 and used DVDs cost \$6.50. . Done.
 Mixture_Word_Problems/276433: if one person can do a job in 8 hours, and two people working together can do it in 6 hours, how long would it take the second person to do it alone?1 solutions Answer 201448 by oberobic(2304)   on 2010-03-02 23:10:09 (Show Source): You can put this solution on YOUR website!The key to solving work problems like this is to determine how much of the job each per can do per unit of time. Then you solve how long it will take to total 1 job. . One person can do the job in 8 hr, so he does 1/8 of the job per hour. Two people working together can do the job in 6 hr, so their combined speed is 1/6 of the job per hour. . 1/8 + 1/x = 1/6 1/x = 1/6 - 1/8 1/x = 2/48 = 1/24 So, the second person takes 24 hr to do the job. . Checking how much they get done in 6 hours working together. 6 hr * 1/8 job/hr = 3/4 of the job 6 hr * 1/24 job/hr = 1/4 of the job 3/4 job + 1/4 job = 1 job . Answer: The second person can do the job in 24 hr working alone. . Done
 Age_Word_Problems/276430: Shelly is three years older than Michele. Four years ago the sum of their ages was 67. Find the age of the person now. Can you give me a basic formula to solving most Age Word Problems. 1 solutions Answer 201447 by oberobic(2304)   on 2010-03-02 23:02:51 (Show Source): You can put this solution on YOUR website!S = Shelly's age M = Michele's age S = M + 3 :: Shelly is 3 years older than Michele. . "Four years ago" their ages will be S-4 and M-4. The sum of their ages was 67. So, today we can say S-4 + M-4 = 67 S + M -8 = 67 S + M = 75 . Substitute S = M+3 . (M+3) + M = 75 2M + 3 = 75 2M = 72 M =36 S = M+3 = 39 . Four years ago their ages were: S = 39 -4 = 35 M = 36 - 4 = 32 . Checking if the sum 4 years ago = 67. 35 + 32 = 67 Yes. . Answer: Shelly is 39, and Michele is 36. . Done
 Linear_Equations_And_Systems_Word_Problems/272540: the sum of three times a number and 7 more than the number is the same as the difference between -11 and twice the number help solve...1 solutions Answer 199343 by oberobic(2304)   on 2010-02-21 21:56:46 (Show Source): You can put this solution on YOUR website!x = the number 3x = three times the number x+7 = 7 more than the number 2x - (-11) = twice the number minus -11 (if that is what you mean?) . 3x + x+7 = 2x - (-11) = 2x+11 4x + 7 = 2x + 11 2x = 4 x = 2 . Checking... 3x + x+7 = 3(2) + 2+7 = 6+9 = 15 2x + 11 = 2(2) + 11 = 15 . So, the number is 2.
 Linear-systems/272564: the length of a rectangle is 5 units longer than its width. The perimeter of this rectangle is 74cm. determine the length and the width of this rectangle.1 solutions Answer 199342 by oberobic(2304)   on 2010-02-21 21:48:59 (Show Source): You can put this solution on YOUR website!L = length W = width P = perimeter = 2L + 2W = 2(L + W) . L = W+5 P = 74 . 2L + 2W = 74 substituting 2(W+5) + 2W = 74 2W + 10 + 2W = 74 4W = 64 W = 16 . L = W+5 = 16+5 = 21 . Checking P = 74 ?? 2(21) + 2(16) = 42 + 32 = 74 Yes. . Answer: L = 21 W = 16 . Done
 Human-and-algebraic-language/272561: The Bon Appetit Bakery makes 4 1/2 times as much revenue on donuts as muffins. If total sales were \$44,000 for May, what dollar amount of each was sold?1 solutions Answer 199340 by oberobic(2304)   on 2010-02-21 21:43:20 (Show Source): You can put this solution on YOUR website!x = donut revenue y = muffin revenue x + y = 44000 so y = 44000 - x . x = 4.5*y . substituting x = 4.5(44000-x) multiply though x = 198000 - 4.5x add 4.5x to both sides 5.5x = 198000 divide both sides by 5.5 x = 36000 . y = 44000 - 36000 = 8000 . Answer: donut revenue = \$36,000 muffin revenue = \$8,000