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 Travel_Word_Problems/276789: A car traveled 50 mph between two towns. If the speed had been 10 mph faster, the trip could have been made in 1 hr. less time. How far apart are the towns?1 solutions Answer 201787 by ankor@dixie-net.com(15638)   on 2010-03-04 08:16:41 (Show Source): You can put this solution on YOUR website!A car traveled 50 mph between two towns. If the speed had been 10 mph faster, the trip could have been made in 1 hr. less time. How far apart are the towns? : Let d = dist between towns : Write a time equation; time = dist/speed : Actual speed time - faster time = 1 hr - = 1 Multiply by 300 6d - 5d = 300 d = 300 mi between towns : Check by finding the times 300/50 = 6 hr 300/60 = 5 hrs
 Graphs/276790: a caterer charges a fixed cost for each person served. you know the cost for 100 will be \$750 and the cost for 150 will be \$1050. fins the caterers fixed cost and the cost per student served.1 solutions Answer 201783 by ankor@dixie-net.com(15638)   on 2010-03-04 07:51:25 (Show Source): You can put this solution on YOUR website!A caterer charges a fixed cost for each person served. You know the cost for 100 will be \$750 and the cost for 150 will be \$1050. Find the caterer's fixed cost and the cost per student served. : Assign the given values as follows: x1=100, y1=750 x2=150, y2=1050 : Find the slope: m = : m = = = 6 is the slope : Find the equation: y - y1 = m(x - x1) y - 750 = 6(x - 100) y - 750 = 6x - 600 y = 6x - 600 + 750 y = 6x + 150, the equation : From this we know the cost per student = \$6, the fixed cost \$150
 Travel_Word_Problems/276733: when the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 13. What is the original number? Can you solve using the 5-step method. Please and thank you!1 solutions Answer 201737 by ankor@dixie-net.com(15638)   on 2010-03-03 22:10:52 (Show Source): You can put this solution on YOUR website!when the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 13. What is the original number? : Let x = the 10's digit Let y = the units then 10x + y = "the number" : Write an equation for each statement: "the digits of a two-digit number are reversed, the new number is 9 more than the original number," 10y + x = 10x + y + 9 Combine like terms 10y - y = 10x - x + 9 9y = 9x + 9 Simplify, divide by 9 y = (x + 1) : "the sum of the digits of the original number is 13." x + y = 13 Substitute (x+1) for y x + (x+1) = 13 2x = 13 - 1 2x = 12 x = 6 is the 10's digit then since the sum is 13, obviously y = 7 is the units and 67 is the original two digit number : Check this in the statement: "when the digits of a two-digit number are reversed, the new number is 9 more than the original number, 76 = 67 + 9 : When the number 67 if reversed it is 9 more than the original
 Travel_Word_Problems/276735: Eddie's age is 4 times Marco's. In 10 years Eddie will be twice as old as Marco will be. How old is each now? This has to be solved in the 5-step Method. Thank you!1 solutions Answer 201728 by ankor@dixie-net.com(15638)   on 2010-03-03 21:23:34 (Show Source): You can put this solution on YOUR website!Eddie's age is 4 times Marco's. In 10 years Eddie will be twice as old as Marco will be. How old is each now? This has to be solved in the 5-step Method. : Let e = E's present age Let m = M's present age : Write an equation for each statement "Eddie's age is 4 times Marco's." e = 4m : "In 10 years Eddie will be twice as old as Marco will be." e + 10 = 2(m + 10) e + 10 = 2m + 20 e = 2m + 20 - 10 e = 2m + 10 Substitute 4m for e from the 1st equation, find m 4m = 2m + 10 4m - 2m = 10 2m = 10 m = 5 yrs is M now and e = 4(5) e = 20 yrs is E now ; Check solution in the statement: "In 10 years Eddie will be twice as old as Marco will be. 20 + 10 = 2(5 + 10) 30 = 2(15) ; The last step is the sentence about this, I will let you do that
 Surface-area/276740: A 20-inch square piece of metal is to be used to make an open-top box by cutting equal-sized squares from each corner and folding up the sides. The length, width, and height of the box are each to be less than 14 inches. What size squares should be cut out to produce a box with volume 550 cubic inches? What size squares should be cut out to produce a box with largest possible volume? 1 solutions Answer 201725 by ankor@dixie-net.com(15638)   on 2010-03-03 21:13:48 (Show Source): You can put this solution on YOUR website!A 20-inch square piece of metal is to be used to make an open-top box by cutting equal-sized squares from each corner and folding up the sides. The length, width, and height of the box are each to be less than 14 inches. What size squares should be cut out to produce a box with volume 550 cubic inches? : Let x = side of the squares to be cut out of the metal : Since the piece of metal is square, the base will be square also Dimensions of the base (20-2x) by (20-2x), the height will be x therefore (20-2x)^2 = (20-2x) = plot these two equations y = 20-2x and y = : Note there are two points of intersection x=2.35, y=15.3; not this one y > 14" and x=4.43, y=11.15; this one will be Ok : We can say 4.43" squares to be cut out of each corner of the metal ; ; Check the vol (20-2(4.43))^2 * 4.43 = 549.76 ~ 550 : : What size squares should be cut out to produce a box with largest possible volume? Graph this equation, volume is on the y axis y = x(20-2x)^2 max volume: x=3.33", y=592.6 cu/in ; We can say 3.33" squares should be cut out each corner for max volume
 Linear_Equations_And_Systems_Word_Problems/276777: An entertainment promotor for a magic show must make \$161,000 from ticket sales in order to cover the cost and make a reasonable profit. The auditorium has 3000 seats with 1800 seats on the lower floor and 1200 balcony seats. Attendes will pay \$20 more for the lower floor seats than for the balcony seats. Write a system of equations with F for the floor seats ticket price and B for the balcony seat ticket price. 1 solutions Answer 201697 by ankor@dixie-net.com(15638)   on 2010-03-03 19:29:12 (Show Source): You can put this solution on YOUR website!show must make \$161,000 from ticket sales in order to cover the cost and make a reasonable profit. The auditorium has 3000 seats with 1800 seats on the lower floor and 1200 balcony seats. Attendees will pay \$20 more for the lower floor seats than for the balcony seats. Write a system of equations with F for the floor seats ticket price and B for the balcony seat ticket price. : Let b = balcony price and f = lower floor price f = (b+20) also : Total revenue equation 1200b + 1800f = 161000 : Simplify, divide by 100 12b + 18f = 1610 : Replace f with (b+20), find b 12b + 18(b+20) = 1610 ; 12b + 18b + 360 = 1610 : 30b = 1610 - 360 b = b = \$41.67 for balcony seat and 41.67 + 20 = \$61.67 for lower floor : : Check solution by finding the actual revenue 1200(41.67) + 1800(61.67) = 50004 + 111006 = \$161,010.00 (an extra \$10 from rounding up the cents)
 Age_Word_Problems/276487: Hannah, Mark and Tom have a combined age of 68. Hannah is twice as old as the di erence between Mark and Tom's age. Mark and Tom's combined age is 16 times Hannah's age. Mark is older than Tom. How old is Tom? (a) 31 (b) 32 (c) 33 (d) 34 (e) None of the above1 solutions Answer 201690 by ankor@dixie-net.com(15638)   on 2010-03-03 19:05:07 (Show Source): You can put this solution on YOUR website!Hannah, Mark and Tom have a combined age of 68. h + m + t = 68 : Hannah is twice as old as the di fference between Mark and Tom's age. h = 2(m - t) : Mark and Tom's combined age is 16 times Hannah's age. m + t = 16h -16h + m + t = 0 : Subtract the above equation from the 1st equation h + m + t = 68 -16h + m + t = 0 -------------------subtraction eliminates m & t, find h 17h = 68 h = h = 4 yrs is Hannah's age : Replace h with 4 in the equation m + t = 16h m + t = 16(4) m + t = 64 : Replace h in the equation h = 2(m-t) 2(m - t) = 4 Simplify, divide by 2 m - t = 2 ; Add the two equation m + t = 64 m - t = 2 ------------- 2m = 66 m = 33 yrs is Marks age then 31 is Tom's age : : Check total 4 + 33 + 31 = 68
 Graphs/276384: PLEASE HELP. A store received two shipments of clothing. the cost of the first shipment, which contains 10 sweaters and 20 jackets was \$800 . the cost of the second shipment, which contains 5 sweaters and 15 jackets, was \$550. find the cost of one sweater and the cost of one jacket.1 solutions Answer 201629 by ankor@dixie-net.com(15638)   on 2010-03-03 16:54:35 (Show Source): You can put this solution on YOUR website!: I assume you are the one that sent this problem to my comment section. There is no way for me to know for sure, who you are unless you give an email address ; Anyway here is solution to this problem : A store received two shipments of clothing. the cost of the first shipment, which contains 10 sweaters and 20 jackets was \$800 . the cost of the second shipment, which contains 5 sweaters and 15 jackets, was \$550. find the cost of one sweater : Let s = cost of one sweater Let j = cost of one jacket : 1st shipment equation 10s + 20j = 800 : 2nd shipment equation 5s + 15j = 550 Put it in a form we can use for substitution 5s = 550 - 15j divide by 5 s = - j s = 110 - 3j : Replace s with (110-3j) is the 1st shipment equation 10s + 20j = 800 10(110-3j) + 20j = 800 1100 - 30j + 20j = 800 -30j + 20j = 800 - 1100 -10j = -300 j = \$30 for jackets : We know s = 110-3J s = 110 - 3(30) s = 110 - 90 s = \$20 for sweaters : : Check solutions in the 2nd shipment equation 5s + 15j = 550 5(20) + 15(30) = 100 + 450 = 550; confirms our solution
 Rate-of-work-word-problems/276491: If 5 adults and 2 children work together, a job can be done in a day. If only 2 adults work, then 6 children must work in order to complete the job in a day. The number of days that it takes for a child to do the job alone is: a 9 b 25/3 c 26/3 d 8 e none of above1 solutions Answer 201625 by ankor@dixie-net.com(15638)   on 2010-03-03 16:28:09 (Show Source): You can put this solution on YOUR website!If 5 adults and 2 children work together, a job can be done in a day. If only 2 adults work, then 6 children must work in order to complete the job in a day. The number of days that it takes for a child to do the job alone is: : Let a = time required when adult does the job alone let c = time required when a child does it : Let the completed job = 1 : + = 1 and + = 1 : Therefore: + = + - = - = Cross multiply 4a = 3c a = c a = .75c : Using the 1st equation replace a with .75c, find c + = 1 Multiply equation by 3c, results 4(5) + 3(2) = 3c 20 + 6 = 3c c = days for a child alone
 Linear_Algebra/276379: please explain this problem step by step. I am very confuse. seting up an equation in two variables for each problme. then solve. A rowing team rowing with the current traveled 18 mi in 2h. against the curret, the team rowed a distance of 8 mi in the same amount of time. find the rate of the rowing team in calm water and rate of the curreent. PLEASE HELP1 solutions Answer 201431 by ankor@dixie-net.com(15638)   on 2010-03-02 21:40:34 (Show Source): You can put this solution on YOUR website!A rowing team rowing with the current traveled 18 mi in 2h. against the current, the team rowed a distance of 8 mi in the same amount of time. find the rate of the rowing team in calm water and rate of the current : Let r = the rowing rate in still water Let c = rate of the current then (r+c) = speed downstream and (r-c) = speed upstream : Write a distance equation for each way. Dist = speed * time (2hrs for both) 2(r+c) = 18; (downstream) 2(r-c) = 8: (upstream) ; Multiply what's inside brackets in both equations, then use elimination: 2r + 2c = 18 2r - 2c = 8 ----------------adding eliminates c, find r 4r + 0c = 26 4r = 26 r = r = 6.5 mph rowing speed in still water : Find c using the equation 2r + 2c = 18, substitute 6.5 for r 2(6.5) + 2c = 18 13 + 2c = 18 2c = 18 - 13; subtract 13 from both sides 2c = 5 c = c = 2.5 mph is the rate of the current : : Check solutions in the original upstream equation, substitute for r and c 2(r-c) = 8: 2(6.5 - 2.5) = 8 2(4) = 8; confirms our solution : : Did this unconfuse you, any questions, ankor@att.net
 Linear-systems/276359: Four times the difference of a number and one is equal to six times the sum of the number and three. Find the number. Thank you!1 solutions Answer 201428 by ankor@dixie-net.com(15638)   on 2010-03-02 21:23:00 (Show Source): You can put this solution on YOUR website!let x = "a number : Just write an equation for what it says: "Four times the difference of a number and one is equal to six times the sum of the number and three." 4(x-1) = 6(x+3) 4x - 4 = 6x + 18 4x - 6x = 18 + 4 -2x = 22 x = x = -11 ; : See if that's true! 4(-11-1) = 6(-11 + 3) 4(-12) = 6(-8), it is
 Human-and-algebraic-language/276295: The sum of two numbers is 80. If the larger is divided by the smaller, the quotient is 7, and the remainder is 8. Find the numbers. 1 solutions Answer 201388 by ankor@dixie-net.com(15638)   on 2010-03-02 19:23:33 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 80. x + y = 80 y = (80-x) : If the larger is divided by the smaller, the quotient is 7, and the remainder is 8 = 7 7y = x - 8 replace y with (80-x) 7(80-x) = x - 8 : 560 - 7x = x - 8 : 560 + 8 = x + 7x : 568 = 8x x = x = 71 then y = 9, obviously : : divide 71 by 9: 7 remainder 8 x = 71
 Volume/276248: How do you find the volume of a sewer pipe 100 ft long with a radius of 24 in with the answer equaling 1256.68ft3?1 solutions Answer 201383 by ankor@dixie-net.com(15638)   on 2010-03-02 19:06:45 (Show Source): You can put this solution on YOUR website!How do you find the volume of a sewer pipe 100 ft long with a radius of 24 in with the answer equaling 1256.68ft3? : The vol of a cylinder : change 24" to 2 ft
 Geometry_Word_Problems/276252: the volumes of two similar solids, A and B, are in the ratio 1:64,respectively.What is the ratio of the surface area of solid A to the surface area of solid B? Can you please express it in a common fraction? 1 solutions Answer 201368 by ankor@dixie-net.com(15638)   on 2010-03-02 18:13:39 (Show Source): You can put this solution on YOUR website!the volumes of two similar solids, A and B, are in the ratio 64,respectively. What is the ratio of the surface area of solid A to the surface area of solid B? Can you please express it in a common fraction? : Assume they are cubes Let x = side of the smaller Let y = side of the larger : = cross multipl Find the cube root of both sides y = 4x : Surface area ratio Replace y with 4x Cancel the 6 = cancel x^2 is the surface area fraction
 Miscellaneous_Word_Problems/276055: A farmer spends \$4,000 to obtain 100 head of livestock.Prices are: calves – \$120 each; lambs – \$50 each; piglets – \$25 each. If he purchased at least one animal of each type and fewer than 10 calves,how many lambs did he buy? a 44 b 46 c 48 d 50 e None of the above1 solutions Answer 201325 by ankor@dixie-net.com(15638)   on 2010-03-02 16:26:00 (Show Source): You can put this solution on YOUR website!A farmer spends \$4,000 to obtain 100 head of livestock.Prices are: calves – \$120 each; lambs – \$50 each; piglets – \$25 each. If he purchased at least one animal of each type and fewer than 10 calves,how many lambs did he buy? ; Total animal equation: C + L + P = 100 : Total cost equation 120C + 50L + 25P = 4000 Simplify, divide by 5 24C + 10L + 5P = 800 : Multiply the 1st equation by 5 subtract from the above, get rid of the pigs! 24C + 10L + 5P = 800 5C + 5L + 5P = 500 -----------------------Subtraction, eliminates p 19C + 5L = 300 5L = 300 - 19C L = - C L = 60 - C : We know L has to be an integer, therefore C has to be a multiple of 5 they tell his their are fewer than 10 Calves so obviously C = 5 L = 60 - 5 L = 60 - 19 L = 41 lambs : Find the pigs 100 - 5 - 41 = 54 pigs : : Check solution by finding the total cost 120(5) + 41(50) + 25(54) = 600 + 2050 + 1350 = 4000
 Sequences-and-series/276177: How do I solve this word problem: Two consecutive positive odd numbers have the property that their product plus the square of their difference equals 147. Find the larger of these two numbers.1 solutions Answer 201319 by ankor@dixie-net.com(15638)   on 2010-03-02 16:03:11 (Show Source): You can put this solution on YOUR website!Two consecutive positive odd numbers x, (x+2) : have the property that their product plus the square of their difference equals 147. x(x+2) + ((x+2) - x)^2 = 147; we know the difference is 2, right? : x^2 + 2x + 2^2 = 147 : x^2 + 2x + 4 - 147 = 0 : x^2 + 2x - 143 = 0 Factors to: (x+13)(x-11) = 0 The positive solution x = 11, then the larger number = 13 : : Check solution in the statement: "their product plus the square of their difference equals 147." (11 * 13) + (13-11)^2 = 147 143 + 2^2 = 147
 Length-and-distance/276161: the patio of a restaurant is enlarged to make room for additional table. the lenght of the patio is increased 2 meters, but the widgh of the patio is not changed. the area of the enlarged patio is 24 squares meter. what was the original area of the patio????????????? 1 solutions Answer 201317 by ankor@dixie-net.com(15638)   on 2010-03-02 15:52:31 (Show Source): You can put this solution on YOUR website!the patio of a restaurant is enlarged to make room for additional table. the lenght of the patio is increased 2 meters, but the widgh of the patio is not changed. the area of the enlarged patio is 24 squares meter. what was the original area of the patio? : Original dimensions: L by W; New dimensions: (L+2) by W : New area: W(L+2) = 24 WL + 2W = 24 WL = 24-2W Old area = WL therefore old area = 24-2W :
 Volume/276163: How many gallons are in a cylinder 2ft tall and 30 in round if we take out 350 gallons?1 solutions Answer 201308 by ankor@dixie-net.com(15638)   on 2010-03-02 14:20:13 (Show Source): You can put this solution on YOUR website!How many gallons are in a cylinder 2ft tall and 30 in round if we take out 350 gallons? : 1 cu/ft = 7.481 gal; 1728 cu/in = 1 cu/ft : Find the radius using the given circumference = 30 r = r = 4.77 inches : Find the vol, Height = 24 inches = 1715.528 cu/inches change to cubic ft, find no. of gal, = 7.427 gal, obviously you can't take out 350
 Travel_Word_Problems/276144: An automobile averaged 45 mph for the first part of a trip and 50 mph for the second part. If the entire trip took 4hr and covered 195 mi, for how long was the rate 45 mph?1 solutions Answer 201306 by ankor@dixie-net.com(15638)   on 2010-03-02 14:03:40 (Show Source): You can put this solution on YOUR website!An automobile averaged 45 mph for the first part of a trip and 50 mph for the second part. If the entire trip took 4hr and covered 195 mi, for how long was the rate 45 mph? : Let x = time at 45 mph then (4-x) = time at 50 mph : Write a distance equation: dist = speed * time : 45mph dist + 50 mph dist = 195 mi 45x + 50(4-x) = 195 : 45x + 200 - 50x = 195 : 45x - 50x = 195 - 200 : -5x = -5 : x = 1 hr at 45 mph : Check solution (3hr at 50mph) 45(1) + 50(3) = 195
 Travel_Word_Problems/275955: Carl and Kyle leave Kyle's house at the same time. Carl drives north and Kyle drives West. Carl's average speed is 9 mph slower than Kyle's. At the end of one hour, they are 45 miles apart. Find the average speed of Kyle. (Round off your answer to the nearest tenth).1 solutions Answer 201259 by ankor@dixie-net.com(15638)   on 2010-03-02 10:20:06 (Show Source): You can put this solution on YOUR website!Carl and Kyle leave Kyle's house at the same time. Carl drives north and Kyle drives West. Carl's average speed is 9 mph slower than Kyle's. At the end of one hour, they are 45 miles apart. Find the average speed of Kyle. (Round off your answer to the nearest tenth). : Let s = K's driving speed then (s-9) = C's driving speed : Solve this as a right triangle: a^2 + b^2 = c^2 where the distance after 1 hr is: a = 1s b = 1(s-9) c = 45 : s^2 + (s-9)^2 = 45^2 A quadratic equation s^2 + s^2 - 18s + 81 = 2025 : 2s^2 - 18s + 81 - 2025 = 0 : 2s^2 - 18s - 1944 = 0 Simplify, divide by 2 s^2 - 9s - 972 = 0 Fortunately this will factor (s - 36)(s + 27) = 0 Positive solution s = 36 mph is K's speed : : Check solution using a calc: Enter: = 45; confirms our solution
 Quadratic_Equations/275837: f(x)4x2 + 4x - 3 I need help to find the intercepts, the vertex and the maximun or minimun. I know I need to use the quadratic formula, but I don't know how to apply it to find these three points. Thank you for your help. Martha1 solutions Answer 201253 by ankor@dixie-net.com(15638)   on 2010-03-02 10:03:59 (Show Source): You can put this solution on YOUR website!f(x) = 4x2 + 4x - 3 I need help to find the intercepts, the vertex and the maximum or minimum. y = 4x^2 + 4x - 3 The y intercept occurs when x=0 y = 4(0) + 4(0) - 3 y = -3 is the y intercept : You can use the quadratic formula to find the x intercepts In this equation a=4, b=4, c=-3 : : : Two solutions x = x = .5 and x = x = -1.5 : The x intercepts: x=.5, x=-1.5 : Find the vertex, first find the axis of symmetry using the formula x = -b/(2a) x = x = -.5 The vertex occurs at x=-.5 : Substitute that in the original equation for find y y = 4(-.5^2) + 4(-.5) - 3 y = 4(.25) -2 - 3 y = +1 - 2 - 3 y = -4 : Vertex: x=-.5,y=-4; and it is a minimum : Looks like this : The intercepts and vertex should be apparent when you see it on this graph
 Radicals/275940: How do I solve this equation 2x + sqrt(x) -1 = 0 for all real numbers?1 solutions Answer 201242 by ankor@dixie-net.com(15638)   on 2010-03-02 09:33:49 (Show Source): You can put this solution on YOUR website!How do I solve this equation 2x + sqrt(x) -1 = 0 for all real numbers? : 2x + sqrt(x) - 1 = 0 : sqrt(x) = -2x + 1 Square both sides x = (-2x+1)^2 : x = 4x^2 - 4x + 1 : 0 = 4x^2 - 4x -x + 1 : 0 = 4x^2 - 5x + 1 Factor (4x - 1)(x - 1) = 0 Two solutions x = 1 and x = .25 : Check both solutions in original equation. Only x = .25 satisfies the equation
 Numbers_Word_Problems/275875: if the average of three different positive integers is 60, what is the greatest possible value of one of the integers?1 solutions Answer 201216 by ankor@dixie-net.com(15638)   on 2010-03-02 07:57:06 (Show Source): You can put this solution on YOUR website!if the average of three different positive integers is 60, what is the greatest possible value of one of the integers? : 3 * 60 = 180 would be the total of the 3 integers 177 would be the greatest possible value = 60
 Miscellaneous_Word_Problems/275890: After the first day of registration, 54 students are enrolled in summer camp program. If 60% of the slots are now filled, how many slots were available? And what would the equation be?1 solutions Answer 201192 by ankor@dixie-net.com(15638)   on 2010-03-01 21:53:26 (Show Source): You can put this solution on YOUR website!After the first day of registration, 54 students are enrolled in summer camp program. If 60% of the slots are now filled, how many slots were available? And what would the equation be? : Let x = no. of slots available : The equation: .60x = 54 x = x = 90 slots,
 Rate-of-work-word-problems/275932: DON CLEAN THE HOUSE IN 3 HOURS. LISA CLEANED IT IN 8 HOURS. HOW LONG WILL IT TAKE THEM TO CLEAN THE HOUSE TOGETHER?1 solutions Answer 201190 by ankor@dixie-net.com(15638)   on 2010-03-01 21:49:52 (Show Source): You can put this solution on YOUR website!DON CLEAN THE HOUSE IN 3 HOURS. LISA CLEANED IT IN 8 HOURS. HOW LONG WILL IT TAKE THEM TO CLEAN THE HOUSE TOGETHER? : Let t = time required working together : Let the completed job = 1 (a clean house) : Each will do a fraction of the job, the two fractions add up to 1 + = 1 Multiply the equation by 24 to clear the denominators, results 8t + 3t = 24(1) 11t = 24 t = hrs or 2 hrs + (*60) ~ 11 min
 Geometry_Word_Problems/275915: The length of a rectangle is 2 cm more than three times the width. Find the dimensions of this rectangle if the area is 21 cm^2. I found the answer by trial and error (9 & 2 1/3) but I need to know how to actually figure it out and show work. Is there another way besides just plugging in numbers? Thank you!1 solutions Answer 201184 by ankor@dixie-net.com(15638)   on 2010-03-01 21:34:35 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 2 cm more than three times the width. Find the dimensions of this rectangle if the area is 21 cm^2. : There is, and it's pretty easy : Write an equation for each statement "The length of a rectangle is 2 cm more than three times the width." L = 3W + 2 and " the area is 21 cm^2. " L * W = 21 : Replace L with (3W+2) from the 1st statement (3W + 2) * W = 21 3W^2 + 2W - 21 = 0 A quadratic equation we can factor (3W - 7)(W + 3) = 0 The positive solution 3W = 7 W = W = 2 is the width : Find the length using L = 3W + 2 L = 3() + 2 L = 7 + 2 L = 9 ; : Check solutions by finding the area 9 * = 21