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 Numbers_Word_Problems/398107: A two digit number is 4 times the sum of its digits and twice the product of its digit.FIND THE NUMBER1 solutions Answer 282196 by ankor@dixie-net.com(15623)   on 2011-01-22 19:20:22 (Show Source): You can put this solution on YOUR website!two digits, x & y 10x + y = the number : A two digit number is 4 times the sum of its digits 10x + y = 4(x+y) 10x + y = 4x + 4y 10x - 4x = 4y - y 6x = 3y divide both sides by 3 2x = y " and twice the product of its digit." 10x + y = 2xy Replace y with 2x 10x + 2x = 2*x*2x 12x = 4x^2 Divide both sides by 4x 3 = x then y = 2(3) y = 6 : the number = 36 : You can confirm this in both statement: 36 = 4(3+6) and 36 = 2(3*6)
 Travel_Word_Problems/398166: Two bicyclists, 42 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 15 miles per hour and the other 20 miles per hour. At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 38 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet? 1 solutions Answer 282171 by ankor@dixie-net.com(15623)   on 2011-01-22 17:57:23 (Show Source): You can put this solution on YOUR website!Two bicyclists, 42 miles apart, begin riding toward each other on a long straight avenue. One cyclist travels 15 miles per hour and the other 20 miles per hour. : Find their travel time (t) when they meet 20t + 15t = 42 t = 42/35 t = 1.2 hrs : At the same time, Spot (a greyhound), starting at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 38 miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet? : Dog travels 38 mph for 1.2 hrs: 1.2*38 = 45.6 mi
 Travel_Word_Problems/398162: A boat travels 27 miles downstream in 3 hours, and when traveling upstream it takes twice as much time to travel 2/3 of that distance. Find the rate of the boat in still water and the rate of the current.1 solutions Answer 282169 by ankor@dixie-net.com(15623)   on 2011-01-22 17:49:24 (Show Source): You can put this solution on YOUR website!A boat travels 27 miles downstream in 3 hours, and when traveling upstream it takes twice as much time to travel 2/3 of that distance. Find the rate of the boat in still water and the rate of the current. : Find the upstream distance: *27 = 18 miles : Let s = boat speed in still water Let c = current speed then (s-c) = effective speed upstream and (s+c) = effective speed downstream : Write a distance equation for each way : 3(s+c) = 27 6(s-c) = 18 Simplify both equations, divide the 1st by 3, and the 2nd by 6, results: s + c = 9 s - c = 3 ------------addition eliminates c, find s 2s = 12 s = 6 mph is the boat speed in still water and 6 + c = 9 c = 3 mph is the current speed : : Check solutions by finding the distance 3(6+3) = 27 6(6-3) = 18
 Quadratic_Equations/398138: word problem associated with quadratic equation chapter:: a motorboat maintained a constant speed of 12 mph relative to the water going 23 miles upstream then returning. Total time for the trip was 24 hours. Using this information provided, what is the speed of the current in mph?1 solutions Answer 282133 by ankor@dixie-net.com(15623)   on 2011-01-22 15:24:04 (Show Source): You can put this solution on YOUR website!a motorboat maintained a constant speed of 12 mph relative to the water going 23 miles upstream then returning. Total time for the trip was 24 hours. Using this information provided, what is the speed of the current in mph? : Let x = speed of the current then (12-x) = effective speed upstream and (12+x) = effective speed downstream : Write a time equation; time = dist/speed : time upstr + time downstr = 24 hrs + = 24 : Multiply equation by (12-x)(12+x) to get rid of the denominators, results: 23(12+x) + 23(12-x) = 24(12-x)(12+x) : 276 + 23x + 276 - 23x = 24(144 - x^2) : 552 = 3456 - 24x^2 : 24x^2 = 3456 - 552 : 24x^2 = 2904 divide both sides by 24 x^2 = 121 x = x = 11 mph is the speed of the current ; : That seems high, but let's check the time each way 23/(12+11) = 1.0 hr 23/(12-11) = 23 hrs -------------------------- round trip time: 24 hrs, which confirms our solution of x = 11 mph current
 Rate-of-work-word-problems/397946: it takes mang kaloy 3 hrs to plow his ricefield with his new tractor. using the old tractor it takes him 5 hrs. if his son helped him plow the ricefield how long will it take them to plow the ricefield using both tractors1 solutions Answer 282032 by ankor@dixie-net.com(15623)   on 2011-01-21 21:40:36 (Show Source): You can put this solution on YOUR website!it takes mang kaloy 3 hrs to plow his ricefield with his new tractor. using the old tractor it takes him 5 hrs. if his son helped him plow the ricefield how long will it take them to plow the ricefield using both tractors : Let t = time required working together Let the completed job = 1 (a plowed rice field) : + = 1 multiply thru by 15, results 3t + 5t = 15 8t = 15 t = t = 1.875 hrs, or 1 + .875(60) = 1 hr 52.5 min
 Miscellaneous_Word_Problems/397945: The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. b) Find A if \$8300 is invested for 3 years at a simple interest rate of 15%.1 solutions Answer 282029 by ankor@dixie-net.com(15623)   on 2011-01-21 21:33:46 (Show Source): You can put this solution on YOUR website!The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. : a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. A = P(1 + rt) ; b) Find A if \$8300 is invested for 3 years at a simple interest rate of 15%. A = 8300(1 + (.15*3)) A = 8300 * 1.45 A = \$12,035
 Miscellaneous_Word_Problems/398023: A college student has finished 48 credit hours with a GPA of 2.875. To get into the program she wishes to enter, she must have a GPA of 3.0. How many additional credit hours of 4.0 work will raise her GPA to 3.0?1 solutions Answer 282025 by ankor@dixie-net.com(15623)   on 2011-01-21 21:26:18 (Show Source): You can put this solution on YOUR website!A college student has finished 48 credit hours with a GPA of 2.875. To get into the program she wishes to enter, she must have a GPA of 3.0. How many additional credit hours of 4.0 work will raise her GPA to 3.0? : Let c = no. of 4.0 credit hours required to have a 3.0 : = 3.0 Multiply both sides by(c+48), results: 48(2.875) + 4c = 3(c+48) : 138 + 4c = 3c + 144 : 4c - 3c = 144 - 138 : c = 6 credit hrs at 4.0 : : Check this = = 3
 Travel_Word_Problems/397878: A man can run 3 kilometers faster than he walks. It takes him 4 hours to run 30 kilometers. How long would it take him to walk the same distance?1 solutions Answer 281987 by ankor@dixie-net.com(15623)   on 2011-01-21 18:02:26 (Show Source): You can put this solution on YOUR website!: A man can run 3 kilometers faster than he walks. It takes him 4 hours to run 30 kilometers. How long would it take him to walk the same distance? : Let w = his walking speed then (w+3) = his running speed : Therefore: (s+3) = 4(w+3) = 30 4w + 12 = 30 4w = 30 - 12 w = w = 4.5 km/hr is his walking speed therefore: = 6 hrs to walk it
 Metalworking/397899: Please help me solve this equation : the square root of 5z multiplied by the square root of 5 minus the squareroot of z1 solutions Answer 281981 by ankor@dixie-net.com(15623)   on 2011-01-21 17:46:16 (Show Source): You can put this solution on YOUR website! the square root of 5z multiplied by the square root of 5 minus the squareroot of z : I don't see an equal sign here so it is not an equation, we can try to simplify it. which is like terms,
 Linear_Equations_And_Systems_Word_Problems/397901: If in 5 days a clerk can copy 125 pages, 36 lines/page, 11 words/line, how many pages of 30 lines each and 12 words per line can he copy in 6 days? -- The answer is 165, but how do I get there? Thank you!1 solutions Answer 281978 by ankor@dixie-net.com(15623)   on 2011-01-21 17:38:12 (Show Source): You can put this solution on YOUR website!If in 5 days a clerk can copy 125 pages, 36 lines/page, 11 words/line, how many pages of 30 lines each and 12 words per line can he copy in 6 days? : Find how many words per day he can copy = 9900 words per day : In six days: 6 * 9900 = 59400 words : Find the no. of 12 word lines: = 4950 lines : Find no. of 30 line pages: = 165 pages
 Mixture_Word_Problems/397861: A guy has five rings, each weighing 11 g, made of an alloy of 15% silver and 85% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 55%. How much silver should he add?1 solutions Answer 281951 by ankor@dixie-net.com(15623)   on 2011-01-21 16:40:37 (Show Source): You can put this solution on YOUR website!A guy has five rings, each weighing 11 g, made of an alloy of 15% silver and 85% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 55%. How much silver should he add? : Total weight: 5 * 11 = 55 grams : Let s = amt of silver required When 55% gold is obtained, silver content will be 45% : Write a percent silver equation .15(55) + s = .45(s+55) 8.25 + s = .45s + 24.75 s - .45s = 24.75 - 8.25 .55s = 16.5 s = s = 30 grams of silver to be added : : Check .15(55) + 30 = .45(30 + 55) 8.25 + 30 = .45(85) 38.25 = 38.5, confirms our solution of 30 grams of silver
 test/397937: This is my algebra 2 question. It says to find the value of x. Area of rectangle=36cm2. Xcm and (x+5) how do u get the answer 4.1 solutions Answer 281947 by ankor@dixie-net.com(15623)   on 2011-01-21 16:27:33 (Show Source): You can put this solution on YOUR website!his is my algebra 2 question. It says to find the value of x. Area of rectangle=36cm2. Xcm and (x+5) how do u get the answer 4. : Assume you mean the rectangle is x by (x+5), so you have x*(x+5) = 36 x^2 + 5x - 36 = 0 Factors to (x+9)(x-4) = 0 the positive solution x = 4
 Systems-of-equations/397758: Write a system of equations to solve the following problem. Let c be the number of child tickets and a be the number of adult tickets. Each child ticket for a ride costs \$3, while each adult ticket costs \$5. If the ride collected a total of \$150, and 40 tickets were sold, how many of each type of ticket was sold?1 solutions Answer 281929 by ankor@dixie-net.com(15623)   on 2011-01-21 15:43:55 (Show Source): You can put this solution on YOUR website!Write a system of equations to solve the following problem. Let c be the number of child tickets and a be the number of adult tickets. Each child ticket for a ride costs \$3, while each adult ticket costs \$5. If the ride collected a total of \$150, and 40 tickets were sold, how many of each type of ticket was sold? : Two equations: c + a = 40 a = (40-c); use this for substitution and 3c + 5a = \$150
 Length-and-distance/397681: Rachel and Josie live in the cities 500 miles apart. They leave their home at the same time and travel toward each other at the rate of 40mph and 45mph. If they leave at 9 A.M. at what time will they still be 75 miles apart?1 solutions Answer 281927 by ankor@dixie-net.com(15623)   on 2011-01-21 15:39:09 (Show Source): You can put this solution on YOUR website!Rachel and Josie live in the cities 500 miles apart. They leave their home at the same time and travel toward each other at the rate of 40mph and 45mph. If they leave at 9 A.M. at what time will they still be 75 miles apart? : Let t = time they will be 75 mi apart : Write a distance equation: dist = speed * time 40t + 45t = (500 - 75) 85t = 425 t = t = 5 hrs: 9 Am + 5 hrs = 2:00 PM, they will be 75 mi apart : : Check this by finding each travel distance 5*40 = 200 mi 5*45 = 225 mi -------------- total: 425 mi; still have 75 mi to cover the total of 500 mi
 Surface-area/397920: If 2 square feet of a fence can be painted in 10 minutes, how long will it take to paint 150 feet (squared) of fence? NOTE: The base of the fence is 25 ft long and the height is 6 ft. This is my work: (2 sq ft=10 minutes) 150 ft=750 minutes 750 min/10 minutes=75 minutes= 1hr15min*2=2hrs30min1 solutions Answer 281926 by ankor@dixie-net.com(15623)   on 2011-01-21 15:28:57 (Show Source): You can put this solution on YOUR website!If 2 square feet of a fence can be painted in 10 minutes, how long will it take to paint 150 feet (squared) of fence? NOTE: The base of the fence is 25 ft long and the height is 6 ft. : If 2 sq/ft require 10 min, then 1 sq/ft required 5 min therefore 150*5 = 750 min, right?
 test/397803: What is the most important part of elementary algebra1 solutions Answer 281921 by ankor@dixie-net.com(15623)   on 2011-01-21 15:17:50 (Show Source): You can put this solution on YOUR website!Doing it!
 Polynomials-and-rational-expressions/397800: Multiply. 1 solutions Answer 281919 by ankor@dixie-net.com(15623)   on 2011-01-21 15:16:19 (Show Source): You can put this solution on YOUR website! Square stuff, then: (16x^2)(4x^6) = 64x^8