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 Linear-systems/188144: The average life expectancy for American men born in 1900 was 55 years. Life expectancy has increased by about 0.2 year for each birth year after 1900. If this trend continues, for which birth year will the average life expentancy be 91 years? I think the answer is 2080. I just have no idea how to put this in algebraic terms.1 solutions Answer 141293 by ankor@dixie-net.com(15622)   on 2009-03-26 17:04:04 (Show Source): You can put this solution on YOUR website!The average life expectancy for American men born in 1900 was 55 years. Life expectancy has increased by about 0.2 year for each birth year after 1900. If this trend continues, for which birth year will the average life expectancy be 91 years? : Using the form: y = mx + b From the given information we can say the slope (m) of the equation will be +.2 (slope is rise/run; it goes up .2 for each year) : the y intercept (b) will be 55, so we have y = .2x + 55 Where y = life expectancy x years after 1900 : "If this trend continues, for which birth year will the average life expectancy be 91 years?" replace y with 91, solve for x .2x + 55 = 91 .2x = 91 - 55 .2x = 36 x = x = 180 yrs after 1900 which is 2080, so you thought correctly.
 Travel_Word_Problems/188297: John and Mike have been friends since school but haven't seen each other in many years, so they agree to meet one Saturday. John leaves his house at 10:00am and drives east at 50 miles per hour. Mike leaves his house at the same time and drives west at 45 miles per hour. If their houses are connected by a straight highway running east-west (no stoplights or towns in the way) and are 350 miles apart then (a) how far from John's house will they meet? (b) at what time will they meet?1 solutions Answer 141269 by ankor@dixie-net.com(15622)   on 2009-03-26 15:12:53 (Show Source): You can put this solution on YOUR website! John leaves his house at 10:00am and drives east at 50 miles per hour. Mike leaves his house at the same time and drives west at 45 miles per hour. If their houses are connected by a straight highway running east-west (no stoplights or towns in the way) and are 350 miles apart then: : (a) how far from John's house will they meet? Let x = distance from John's house (and distance driven by John) then (350-x) = distance driven by Mike : When they meet they will have driven a total of 350 mi: Their travel times will be the same; write a time equation; Time = John's travel time = Mike's travel time = Cross multiply: 45x = 50(350-x) : 45x = 17500 - 50x : 45x + 50x = 17500 x = x = 184.21 mi from John's house, they will meet : (b) at what time will they meet? Find the travel time of each = 3.68 hrs which is 3 + .68(60) = 3 hr 41 min 10 am + 3hr 41min = 1:41 pm : ; We can confirm our solution by finding Mikes travel time, it should equal John's = 3.68 hrs also
 Travel_Word_Problems/188368: This question is from textbook Prentice Hall: Algebra 1: California edition An airplane flew for 4.23 hours with a 25.5-km/h tail wind. The return flight against the same wind took 4.97 hours. Find the speed of the plane in still air.1 solutions Answer 141256 by ankor@dixie-net.com(15622)   on 2009-03-26 13:14:38 (Show Source): You can put this solution on YOUR website!An airplane flew for 4.23 hours with a 25.5-km/h tail wind. The return flight against the same wind took 4.97 hours. Find the speed of the plane in still air. : Let s = speed of the plane in still air then (s+25.5) = ground speed with the wind and (s-25.5) = ground speed against the wind : The distance there and back is equal, write a dist equation; Dist = time * speed : 4.23(s+25.5) = 4.97(s-25.5) 4.23s + 107.865 = 4.97s - 126.735 107.865 + 126.735 = 4.97s - 4.23s 234.6 = .74s s = s = 317.03 km/hr speed in still air ; ; Check solution by finding the distances: 4.23(317.03+25.5) = 4.97(317.03-25.5) 4.23(342.53) = 4.97(291.53) 1448.9 = 1448.9
 Rate-of-work-word-problems/188347: This question is from textbook It takes Terry 2 hours longer to do a certain job than it takes Tom. They worked together for 3 hours; then Tom left and Terry finished the job in 1 hour. How long would it take each of them to do the job alone. thanks, I will be able to solve it once I know how to set it up.1 solutions Answer 141201 by ankor@dixie-net.com(15622)   on 2009-03-25 21:58:32 (Show Source): You can put this solution on YOUR website!It takes Terry 2 hours longer to do a certain job than it takes Tom. They worked together for 3 hours; then Tom left and Terry finished the job in 1 hour. How long would it take each of them to do the job alone. : let x = time required by Tom then (x+2) = time required by Terry : Let the completed job = 1 : Solve this equation (Terry worked a total of 4 hrs): + = 1
 Rate-of-work-word-problems/188348: This question is from textbook Suppose that Arlene can mow the entire lawn in 40 minutes less time with the power mower than she can with the push mower. One day the power mower broke down after she had been mowing for 30 minutes. She finished the lawn with the push mower in 20 minutes. How long does it take Arlene to mow the entire lawn with the power mower?1 solutions Answer 141200 by ankor@dixie-net.com(15622)   on 2009-03-25 21:52:22 (Show Source): You can put this solution on YOUR website!Suppose that Arlene can mow the entire lawn in 40 minutes less time with the power mower than she can with the push mower. One day the power mower broke down after she had been mowing for 30 minutes. She finished the lawn with the push mower in 20 minutes. How long does it take Arlene to mow the entire lawn with the power mower: : Let t = time required to mow the lawn with the power mower (in minutes) then (t+40) = time required with the push mower : Let the completed job = 1 ; + = 1 multiply equation by t(t+40) to get rid of the denominators, results: 30(t+40) + 20t = t(t+40) : 30t + 1200 + 20t = t^2 + 40t : 50t + 1200 = t^2 + 40t : 0 = t^2 + 40t - 50t - 1200 A quadratic equation: t^2 - 10t - 1200 = 0 Factors to: (t - 40)(t + 30) = 0 Positive solution is what we want here: t = 40 minutes to mow the lawn with power ; : Check solution: + = + = 1
 Linear_Equations_And_Systems_Word_Problems/188293: Mr. Carlson took 2.5 hours to fly his airplane a distance of 360 miles against a steady wind. It took him 2 hours to make the return trip with the wind. Find Mr. Carlons rate in calm air, and the rate of the wind . use r=d/t. answer: Mr. Carlson files 162 miles per hourin calm air; the wind is blowing at a rate of 18 mph. need a full break down of how my book got this answer 1 solutions Answer 141153 by ankor@dixie-net.com(15622)   on 2009-03-25 15:53:55 (Show Source): You can put this solution on YOUR website!Mr. Carlson took 2.5 hours to fly his airplane a distance of 360 miles against a steady wind. It took him 2 hours to make the return trip with the wind. Find Mr. Carlson's rate in calm air, and the rate of the wind. use r=d/t. : Let r = his speed in calm air Let w = the speed of the wind then (r+w) = his ground speed with the wind and (r-w) = his ground speed against the wind : Write a distance equation for each trip: Dist = time * speed 2.5(r-w) = 360 2.0(r+w) = 360 Simplify both equations, divide the 1st by 2.5 and the second by 2, results: r - w = 144 r + w = 180 -------------Addition eliminates w, find r 2r = 324 r = r = 162 mph in still air : and using r + w = 180, find w 162 + w = 180 w = 180 - 162 w = 18 mph is the wind ; : Check solutions in the 1st original equation 2.5(162 - 18) = 2.5(144) = 360 mi, confirms our solutions
 Linear_Equations_And_Systems_Word_Problems/188292: David bought 3 hamburgers and 2 servings of french fries at Diane's Drive -Up for \$6.25. If a serving of fries costs .25 cents more then a hamburger, what is the cost of each? answer: The hamburgers at Diane's cost \$ 1.15 ;the fries cost \$1.40. need a full break down of how my text book got hamburgers \$1.15 and fries \$1.40 as an answer 1 solutions Answer 141147 by ankor@dixie-net.com(15622)   on 2009-03-25 15:33:47 (Show Source): You can put this solution on YOUR website!David bought 3 hamburgers and 2 servings of french fries at Diane's Drive -Up for \$6.25. If a serving of fries costs .25 cents more then a hamburger, what is the cost of each? : Let h = cost of a hamburger Let f = cost of an order of fries : Write an equation for each statement "David bought 3 hamburgers and 2 servings of french fries at Diane's Drive -Up for \$6.25." 3h + 2f = 6.25 : "If a serving of fries costs .25 cents more then a hamburger," f = h + .25 : what is the cost of each? : we know; 3h + 2f = 6.25 Substitute (h+.25) for f in this equation: 3h + 2(h+.25) = 6.25 3h + 2h + .50 = 6.25 5h = 6.25 - .50 5h = 5.75 h = h = \$1.15 for a hamburger : Find f using the 1st equation; f = h + .25 f = 1.15 + .25 f = \$1.40 for fries ; : you can prove it to yourself: 3h + 2f = 6.25, therefore: 3(1.15) + 2(1.40) = 3.45 + 2.80 = 6.25
 Rational-functions/188199: This question is from textbook algebra 2 with trigonomtry what is the square root of x minus 2 minus 7 equals negative 41 solutions Answer 141141 by ankor@dixie-net.com(15622)   on 2009-03-25 14:31:07 (Show Source): You can put this solution on YOUR website!the square root of x minus 2 minus 7 equals negative 4 Assume the problem is: = -4 : Add 7 to both sides: = -4 + 7 = 3 Square both sides; x - 2 = 9 x = 9 + 2 x = 11 : : Check solution in original equation = -4 = -4
 Linear_Equations_And_Systems_Word_Problems/188127: A man walk a certain distance at certain rate. Had he walked 1/2 km an hour faster he would have taken 1 hour less, but he had gone 1 km an hour slower, he would have taken 3 hour longeer. find the distance he travelled and his original rate.1 solutions Answer 141138 by ankor@dixie-net.com(15622)   on 2009-03-25 13:39:02 (Show Source): You can put this solution on YOUR website!A man walk a certain distance at certain rate. Had he walked 1/2 km an hour faster he would have taken 1 hour less, but he had gone 1 km an hour slower, he would have taken 3 hour longer. find the distance he traveled and his original rate. : let d = distance traveled : let r = original rate of travel and d/r = actual time : then (r-1) = the slower rate and (r+.5) = the faster rate : Write Two time equations; Time = Eq1; slower time - actual time = 3 hr - = 3 multiply equation by r(r-1) to get rid of the denominators, results: dr - d(r-1) = 3r(r-1) dr - dr + d = 3r^2 - 3r d = 3r^2 - 3r : eq2; actual time - fast time = 1 hr - = 1 Multiply equation by r(r+.5) to get rid of the denominator, results d(r+.5) - dr = r(r+.5) dr + .5d - dr = r^2 + .5r .5d = r^2 + .5r Multiply equation by 2 d = 2r^2 + r : d = d, therefore we can say: 3r^2 - 3r = 2r^2 + r Divide equation by r 3r - 3 = 2r + 1 3r - 2r = 1 + 3 r = 4 km/h actual waking speed : Find the distance traveled: d = 2r^2 + r Substitute 4 for r d = 2(4^2) + 4 d = 2(16) + f d = 36 km ; ; Check distance in the 2nd equation d = 3r^2 - 3r Substitute 4 for r d = 3(4^2) - 3(4) d = 48 - 12 d = 36 km : : Confirm times: Actual time = 36/4 = 9 hrs Faster time = 36/4.5 = 8 hrs (1 hr faster) slower time = 36/3 = 12 hrs (3 hrs slower) : : Hope all this made sense to you.
 Travel_Word_Problems/188227: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4 mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?1 solutions Answer 141080 by ankor@dixie-net.com(15622)   on 2009-03-24 21:56:09 (Show Source): You can put this solution on YOUR website!Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4 mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water? : Let s = boat speed in still water then (s-4) = speed upstream and (s+4) = speed down stream : Convert 20 min to hrs: 20/60 = hr : Write a time equation: time = Upstream time = downstream time + 20 minutes (1/3 hr) = + : To clear out these denominators, multiply equation by 3(s+4)(s-4) 3(s+4)(s-4)* = 3(s+4)(s-4)* + *3(s+4)(s-4) Results in : 15(s+4) = 15(s-4) + (s+4)(s-4) : 15s + 60 = 15s - 60 + s^2 - 16 : 0 = 15s - 15s - 60 - 60 + s^2 - 16 : 0 = s^2 - 136 : s^2 = 136 s = s = 11.66 mph speed in still water : : Check solution on calc: (speed up = 7.66 and speed down = 15.66) 5/7.66 - 5/15.66 = .3333 which is 1/3 of an hr
 Polynomials-and-rational-expressions/188116: (x^-4y^2/x^2y^5)^2 It says to simplify the expression using positive exponents only.1 solutions Answer 141079 by ankor@dixie-net.com(15622)   on 2009-03-24 21:36:17 (Show Source): You can put this solution on YOUR website! : Combine the exponents of like terms in a manner that will ensure positive exponents ; When you raise one exponent to another exponent, multiply
 Linear-systems/188181: can you please help me : convert this linear equation to standard form? y=1/2x-2/31 solutions Answer 141050 by ankor@dixie-net.com(15622)   on 2009-03-24 18:52:28 (Show Source): You can put this solution on YOUR website!y = 1/2x - 2/3 : Get rid of the fractions, multiply both sides by 6 6y = 3x - 4 : Subtract 3x from both sides, results -3x + 6y = -4 Multiply equation by -1 to change the signs 3x - 6y = 4
 real-numbers/188065: devon purchased tockets to an air show for 9 adults and 2 childeren. the total cost was 192 dollars. the cost of a child's ticket was 3 dollars less than the cost of an adult's ticket. find the price of an adult's ticket and a child's ticket1 solutions Answer 141037 by ankor@dixie-net.com(15622)   on 2009-03-24 16:53:29 (Show Source): You can put this solution on YOUR website!Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was 192 dollars. The cost of a child's ticket was 3 dollars less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket : Let x = cost of an adult ticket then (x-3) = cost of a child's ticket ; 9x + 2(x-3) = 192 : 9x + 2x - 6 = 192 11x = 192 + 6 11x = 198 x = x = \$18 for an adult ticket then 18 - 3 = \$15 for a child's ticket ; ; Check: 9(18) + 2(15) = 192
 real-numbers/188064: one number is four more than a second number. two times the first number is four more than four times the second number1 solutions Answer 141028 by ankor@dixie-net.com(15622)   on 2009-03-24 15:53:15 (Show Source): You can put this solution on YOUR website!Let x = "one number" Let y = "a second number" : Write an equation for each statement: : "one number is four more than a second number." x = y + 4 : " two times the first number is four more than four times the second number" 2x = 4y + 4 ; From the 1st equation, substitute (y+4) for x in the above equation 2(y + 4) = 4y + 4 2y + 8 = 4y + 4 8 - 4 = 4y - 2y 4 = 2y y = y = 2, the second number and x = 2 + 4 x = 6, a number : : Check solution in 2nd statement: "two times the first number is four more than four times the second number" 2(6) = 4(2) = 4
 Linear_Equations_And_Systems_Word_Problems/188052: I need help badly! Can someone help? The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), as shown in the figure below. The remaining credit after 45 minutes of calls is \$22.80 , and the remaining credit after 64 minutes of calls is \$19.76 . What is the remaining credit after 73 minutes of calls?1 solutions Answer 141025 by ankor@dixie-net.com(15622)   on 2009-03-24 15:37:04 (Show Source): You can put this solution on YOUR website!The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes), as shown in the figure below. The remaining credit after 45 minutes of calls is \$22.80 , and the remaining credit after 64 minutes of calls is \$19.76. What is the remaining credit after 73 minutes of calls? ; Not sure what figure you are referring to, write an equation from the given values: Assign the values as follows x1 = 45; y1 = 22.80 x2 = 64; y2 = 19.76 : Find the slope (m) using the formula: m = m = = m = -.16 : Write the equation using the point/slope formula: y - y1 = m(x - x1) y - 22.80 = -.16(x - 45) y - 22.80 = -.16x + 7.2 y = -.16x + 7.2 + 22.80 y = -.16x + 30 ; Use this equation to find the credit (y) when minutes (x) = 73 y = -.16(73) + 30 y = -11.68 + 30 y = \$18.32; credit after 73 minute of calls : : That you can also see the original value of the phone card: x=0, y = \$30 ; : Did this help you understand what's going on here? Any questions
 Exponents-negative-and-fractional/188132: SOLVE BY FACTORING CHECK BOTH ROOTS x = 10/X-31 solutions Answer 141020 by ankor@dixie-net.com(15622)   on 2009-03-24 15:10:33 (Show Source): You can put this solution on YOUR website!x = multiply both sides by (x-3), results: x(x-3) = 10 : x^2 - 3x = 10 : x^2 - 3x - 10 = 0 Factors to: (x-5)(x+2) = 0 Two solutions: x = +5 x = -2 ; : Check both in original equation: 5 = and -2 =
 Expressions-with-variables/188130: This question is from textbook I have a problem where I need to solve the equation (2/t)= (t/5t-12) and the lcd will be 5t-12, but the answers that I come up with when I work this problem have not matched the answers in the back of the book so far. I think the issue I'm having is when i do the 2/t it seems to me that teh t's will cancel and then I am left with 10-24, but that seems to not work Any help with this would be greatly appreciated!!1 solutions Answer 141017 by ankor@dixie-net.com(15622)   on 2009-03-24 15:04:24 (Show Source): You can put this solution on YOUR website! = Cross multiply 2(5t-12) = t^2 : 10t - 24 = t^2 : 0 = t^2 - 10t + 24 A quadratic equation that can be factored to: (t-4)(t-6) = 0 two solutions: t = +4 and t = +6 : : Check both solutions in original problem x=6 = = = You can check solution x=4 in the same way
 test/188084: One third of a certain number exceeds 12 by as much as 100 exceeds the number. What is the number? thanks1 solutions Answer 140974 by ankor@dixie-net.com(15622)   on 2009-03-24 10:15:50 (Show Source): You can put this solution on YOUR website!One third of a certain number exceeds 12 by as much as 100 exceeds the number. What is the number? : Let x = " a certain number" x = 12 + (100-x) ; x = 112 - x Multiply equation by 3 x = 336 - 3x : x + 3x = 336 : 4x = 336 x = x = 84 : : Is that true? *84 = 12 + 100 - 84 28 = 28
 Rate-of-work-word-problems/188003: CAN ANYONE HELP WITH THIS PROBLEM ... I AM SO STUCK!! THANKS Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 700 liters in the pond to start. Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below. 1 solutions Answer 140930 by ankor@dixie-net.com(15622)   on 2009-03-23 19:21:06 (Show Source): You can put this solution on YOUR website!Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 700 liters in the pond to start. Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below. : the equation would be: Total water (W) = 35L*minutes(T) + 700L W = 35T + 700 : Put T on the horizontal (x) and W on the vertical (Y) Graph should look like this: Note when T = 0, you have 700L, when T = 60, you have 35(60)+ 700 = 2800L
 Linear-systems/187937: i want to solve thisimultaneous equation 5x-5y=5,4x-3y=25 i took the first equation x=5+5y/5 and them 4(5-5y)/5-3y=25 i don´t understand the siplpification1 solutions Answer 140928 by ankor@dixie-net.com(15622)   on 2009-03-23 19:08:38 (Show Source): You can put this solution on YOUR website!solve these simultaneous equations: 5x - 5y = 5 4x - 3y = 25 : Take the 1st equation: 5x - 5y = 5 Simplify, divide by 5: x - y = 1 x = y + 1; use this for substitution for x in the 2nd equation: : 4x - 3y = 25 4(y+1) - 3y = 25 4y + 4 - 3y = 25 4y - 3y = 25 - 4 y = 21 : Find x: x = y + 1 x = 21 + 1 x = 22 : : Check solution in the 2nd equation 4(22) - 3(21) = 25 88 - 63 = 25; confirms our solutions
 Equations/187863: This question is from textbook algebra structure and methoed solution to work problem ramon cna do the weekly billing in 2 hrs luann needs three hours. if roman works for 30 minute and then is joined by luann, how long will it take them to finish the tens digit of a two digit number is one more than 3 times the unit digit. subtracting 45 from the number reverses it , find the original number 1 solutions Answer 140898 by ankor@dixie-net.com(15622)   on 2009-03-23 15:45:54 (Show Source): You can put this solution on YOUR website!Ramon can do the weekly billing in 2 hrs; Luann needs three hours. If Romon works for 30 minutes, and then is joined by Luann, how long will it take them to finish? : Let t = amt of time required for them to finish : Change 30 min to .5 hrs : Let the completed job = 1 : + = 1 Multiply equation by 6 to get rid of denominators, results: 3(t+.5) + 2t = 6 : 3t + 1.5 + 2t = 6 : 5t = 6 - 1.5 : 5t = 4.5 t = t = .9 hrs which is .9(60) = 54 min to finish the job ; Check solution: + = + = .7 + .3 = 1 : : the tens digit of a two digit number is one more than 3 times the unit digit. : Let x = the 10's digit, and let y = units then 10x + y = the two digit number : Write an equation for the statement: "the tens digit of a two digit number is one more than 3 times the unit digit." x = 3y + 1 : subtracting 45 from the number reverses it , 10x + y - 45 = 10y + x 10x - x = 10y - y + 45 9x = 9y + 45 Simplify, divide equation by 9 x = y + 5 : find the original number : Substitute (3y+1) for x in the above equation 3y + 1 = y + 5 3y - y = 5 - 1 2y = 4 y = 2 then x = 2 + 5 x = 7 : 72 is our number ; ; Check solution in the statement:"subtracting 45 from the number reverses it" 72 - 45 = 27
 Miscellaneous_Word_Problems/187807: Some US one cent coins are made mostly of copper (each has a mass of 3.1 grams). Some US one cent coins are made mostly of zinc (each has a mass of 2.5 grams). Mr. Kniser has a bag of 1000 US one cent coins. The total mass of the bag is 2616.4 grams. How many of each type of cent is in the bag?1 solutions Answer 140807 by ankor@dixie-net.com(15622)   on 2009-03-22 19:13:58 (Show Source): You can put this solution on YOUR website!Some US one cent coins are made mostly of copper (each has a mass of 3.1 grams). Some US one cent coins are made mostly of zinc (each has a mass of 2.5 grams). Mr. Kniser has a bag of 1000 US one cent coins. The total mass of the bag is 2616.4 grams. How many of each type of cent is in the bag? : Let c = no. of copper coins Let z = no. of zinc coin : A system of two equations: : total no. of coins c + z = 1000 which can be written: c = (1000-z) : and total weight 3.1c + 2.5z = 2616.4 : Substitute (1000-z) for c in the above equation: 3.1(1000-z) + 2.5z = 2616.4 3100 - 3.1z + 2.5z = 2616.4 -.6z = 2616.4 - 3100 -.6z = -483.6 z = z = +806 zinc coins and 1000 - 806 = 194 copper coins ; : Check solution in the weight equation 3.1(194) + 2.5(806) = 601.4 + 2015 = 2616.4