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# Recent problems solved by 'oberobic'

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 Miscellaneous_Word_Problems/510130: Your club is selling candles to raise money. It costs \$100 to rent a booth to sell candles. If the candles cost \$1 each and are sold for \$5 each, how many candle must be sold to equal your expenses?1 solutions Answer 341718 by oberobic(2304)   on 2011-10-05 18:10:03 (Show Source): You can put this solution on YOUR website!Profit = Total Revenue - Total Cost . Total Cost = Variable Cost per Unit * Number of Units Produced + Fixed Costs . Total Revenue = Sales Price * Units Sold . x = number of candles . TC = \$1/candle * x candles + \$100 . TR = \$5/candle * x . We want to find the point where TC =TR, which is the break-even point. . 1x + 100 = 5x 100 = 4x x = 25 . So when you sell 25 candles at \$5, you achieve \$0 profitability. Of course, that means you have paid your fixed costs (\$100). In turn that means the rest of your candles sales contribute profit. . In the following graph, the red line is TC and the green line is TR. .
 Age_Word_Problems/510127: James is three times as old as Carmen. Together, their ages add up to 24. How old is each?1 solutions Answer 341714 by oberobic(2304)   on 2011-10-05 17:57:42 (Show Source): You can put this solution on YOUR website!J = 3*C . J + C = 24 so J = 24-C . substitute . 3*C = 24-C so 4C = 24 C = 6 . J = 3*6 J = 18 . Answer: James is 18,and Carmen is 6. . Done.
 Linear-equations/510120: If x=4, how do you find the slope and y-intercept?1 solutions Answer 341711 by oberobic(2304)   on 2011-10-05 17:54:53 (Show Source): You can put this solution on YOUR website!If x=4 there is no slope and there is no y-intercept. . x=4 defines a vertical line that goes through x=4. . y can take on any value from -infinity to +infinity, but there is no defined slope . Recall the slope = change in y / change in x There is no change in x, so we are attempting to divide by 0. Dividing by zero is undefined. . In slope-intercept form: y = mx+b, the y-intercept is 'b', defining the point (0,b). . But we're told x=4, so there is no point where x=0. . Done.
 Linear_Algebra/510119: y=3x-2 How do you get to the slope? is this right? -2/.6 if this is wrong, how do i get the right answer?1 solutions Answer 341706 by oberobic(2304)   on 2011-10-05 17:49:08 (Show Source): You can put this solution on YOUR website!y = mx + b is in slope-intercept form . m = slope m = change in y / change in x m = coefficient of 'x' in y = mx+b . b = y-intercept, which is the point (0, b) . so... . y = 3x -2 . slope = 3 A positive slope means the line slants up from the lower left to the upper right. With m=3, there is a change of 3 in 'y' for a change of 1 in 'x'. So the line is "rising" 3 times as fast as it is "running." . y-intercept = (0,-2) . To find the x-intercept, simply set y=0 and solve for 'x'. . 0 = 3x -2 add 2 to both sides 2 = 3x so 3x = 2 divide both sides by 3 x = 2/3 . x-intercept = (2/3, 0) .
 Numbers_Word_Problems/510110: The sum of two whole numbers is 19. The product of the number is 84. What are the two numbers? 1 solutions Answer 341705 by oberobic(2304)   on 2011-10-05 17:41:47 (Show Source): You can put this solution on YOUR website!x + y = 19 so x = 19-y . x*y = 84 so x = 84/y . substitute . 84/y + y = 19 . multiply both sides by 'y' . 84 + y^2 = 19y . rearrange . y^2 -19y +84 = 0 . factor . (x-12)(x-7) = 0 . x = 12 or x=7 . which means the other number is either 7 or 12, respectively. . 12*7 = 84 12+7 = 19 Correct. . Answer: The two numbers are 7 and 12. . Done.
 Equations/510114: A=P(1+rt) solve for t1 solutions Answer 341704 by oberobic(2304)   on 2011-10-05 17:35:24 (Show Source): You can put this solution on YOUR website! . . . . . Done.
 Graphs/510113: How do you graph 2x+y=3 and 4x+2y=61 solutions Answer 341703 by oberobic(2304)   on 2011-10-05 17:31:28 (Show Source): You can put this solution on YOUR website!Reformat both equations to slope-intercept form: y=mx+b. Determine two points on each line. Draw the two lines. . 2x + y = 3 y = -2x + 3 (x=0, y= 3) (x=5, y=-7) . 4x + 2y = 6 is 2x + y = 3 which is the same line .
 percentage/510102: Jim bought tickets for \$70 and sold them for \$98, What is the percentage of increase1 solutions Answer 341702 by oberobic(2304)   on 2011-10-05 17:27:55 (Show Source): You can put this solution on YOUR website!To determine percentage change, you calculate: . . in this case, . . Done.
 Travel_Word_Problems/509618: How long will it take you of your going 3 miles per hour, going 2 miles? HELP!1 solutions Answer 341515 by oberobic(2304)   on 2011-10-04 21:14:59 (Show Source): You can put this solution on YOUR website!d = r*t is the fundamental distance equation. . you need to know 2 of these to calculate the 3rd. . 3 mph = r 2 mph = r . but unless you know 'd', you cannot calculate 't' . Say d = 9 . 9 = 3t t = 9/3 = 3 hr : It takes 3 hr at 3 mph to go 9 miles . 9 = 2t t = 9/2 = 4 1/2 : It takes 4 1/2 hr at 2 mph to go 9 miles. . And so forth.
 Linear-equations/509616: Determine if the ordered pairs (0,3),(3,0),(−1,1) are solutions of the equation y = 2x + 31 solutions Answer 341514 by oberobic(2304)   on 2011-10-04 21:11:27 (Show Source): You can put this solution on YOUR website!y = 2x+3 . x = 0, y = 3 : (0,3) x = -1, y = 1 : (-1,1) x = 3, y = 9 : (3,9) NOT (3,0) . Done
 Miscellaneous_Word_Problems/509606: Write an equation and solve for the word problem: Rico spent \$18.50 to rent a lawn mower. The fee for the first hour was \$8. Each additional hour cost \$3.50. For how many hours did he rent the mower? I figured out the answer is 4 hours, but what is the equation that goes with this word problem?1 solutions Answer 341513 by oberobic(2304)   on 2011-10-04 21:09:02 (Show Source): You can put this solution on YOUR website!rental is for 'x' hrs price is 'y' . y = 3.5(x-1) + 8 . y = 3.5x -3.5 + 8 . y = 3.5x + 4.5 . He spent 18.50 . 18.50 = 3.5x + 4.5 3.5x = 18.50 -4.5 x = 14/3.5 x = 4 . check using the facts hr 1 = 8 hr 2, 3 & 4 = 3.50 3*3.50 = 10.5 8 + 10.5 = 18.5 . Answer: He rented it for 4 hr.
 Linear-systems/509582: 3n-2 Divided by 5=7/101 solutions Answer 341503 by oberobic(2304)   on 2011-10-04 20:44:57 (Show Source): You can put this solution on YOUR website! . cross multiply to set up the solution . . . . . . . Check this answer by plugging this value back into the equation. . Correct . . Done.
 test/509583: 10x - (x+3) Simplify the expression1 solutions Answer 341499 by oberobic(2304)   on 2011-10-04 20:34:26 (Show Source): You can put this solution on YOUR website!10x -(x+3) = 10x -x -3 10x -x -3 = 9x - 3 9x -3 = 3(3x -1) . Since we do not have an equation we cannot solve it. . Done.
 Polynomials-and-rational-expressions/509580: what is the answer for 7x-3=4x1 solutions Answer 341498 by oberobic(2304)   on 2011-10-04 20:32:55 (Show Source): You can put this solution on YOUR website!7x - 3 = 4x . add 3 to both sides . 7x -3+3 = 4x +3 . subtract 4x from both sides . 7x -4x = 4x-4x +3 . 3x = 3 . divide both sides by 3 . 3/3x = 3/3 . x = 1 . Check the answer to make sure it's true. . 7(1) -3 = 4(1)? 7-3 = 4 Correct. . Answer: x = 1. . Done.
 Square-cubic-other-roots/509558: A Square floor tile has an area of 64 square yards. How long is each side of the lot?1 solutions Answer 341490 by oberobic(2304)   on 2011-10-04 20:11:08 (Show Source): You can put this solution on YOUR website!sqrt(64) = +8 or -8 . Of course -8 makes no sense. . So the answer is 8 yd.
 Graphs/509549: solve equation for y -6x+y=111 solutions Answer 341489 by oberobic(2304)   on 2011-10-04 20:04:33 (Show Source): You can put this solution on YOUR website!Solve the equation -6x +y = 11 for y . That means to get it into slope-intercept form: y = mx+b . Then you can define two points and draw a line. . You also can define the slope, y-intercept, and x-intercept. . To get started, add 6x to both sides . y -6x + 6x = 11 + 6x . y = 6x + 11 . There is no need to go further. . The slope is 6, which means it goes steeply up to the right. There is a change of 6 in y for a change of 1 in x. . The y-intercept occurs when x = 0, so you can see it is the point: (0, 11). 'b' is the y-intercept . The x-intercept occurs when y = 0. If x=-11/6, then 6x = -11. y = 6(-11/6) + 11 y = 0 This defines the point (-11/6,0). . With two points you can draw a straight line. You also can check the intercepts to see if they cross where they are supposed to. .
 Linear-equations/509540: solve the problem: The worlds largest taco contained approximately 1 kg of onion for every 6.6 kg of grilled steak. The total weight of these two ingredients was 617.6 kg. To the nearest tenth of a kilogram, how many kilograms of each ingredient were used to make the taco? I am struggling with turning the story problem into the actual equation. 1 solutions Answer 341488 by oberobic(2304)   on 2011-10-04 20:02:34 (Show Source): You can put this solution on YOUR website!The ratio of onions to grilled steak was 1:6.6 kg. . In this case, 'k' is simply an constant multiplier. . 1k + 6.6k = 617.6 . 7.6k = 617.6 . k = 617.6/7.6 . k = 81.3 . So the taco contained about 81.3 kg of onions and 6.6*81.3 = 536.3 kg of grilled steak. . Done.