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Word_Problems_With_Coins/214173: I am a parent I want to help my child but i don't know how to do this. I'm not asking for the answer,(but i'm not turning it down either:>), but the necessary steps to take to solve this problem, so I may be able to help her. The question is Joshua had 142 coins, all nickels and quarters. The total amount was $15.30. HOw many coins of each type did he have? Solve this problem with Algebra using variables to stand for the number of nickels and the number of quarters. Thank you so much for whatever help you can provide me with. This question was not in a textebook. 1 solutions Answer 161768 by ankor@dixie-net.com(15638)   on 2009-09-16 15:36:44 (Show Source): You can put this solution on YOUR website! Joshua had 142 coins, all nickels and quarters. The total amount was $15.30. HOw many coins of each type did he have? : Let n = no. of nickels; let q = no. of quarters : write an equation for each statement: : "Joshua had 142 coins," n + q = 142 : "The total amount was $15.30." .05n + .25q = 15.30 : HOw many coins of each type did he have? : Go back to the 1st equation, and arrange it for substitution in the 2nd equation n + q = 142 q = (142-n) : Replace q with (42-n) in the 2nd equation, find n .05n + .25(142-n) = 15.30 : Multiply what's inside the brackets .05n + 35.5 - .25n = 15.30 ; .05n - .25n = 15.30 - 35.50 : -.20n = -20.20 n = ; minus into a minus is plus n = +101 nickels : Find q: q = 142 - 101 q = 41 quarters : : See if this is right, substitute for n and q .05(101) + .25(41) = 15.30 5.05 + 10.25 = 15.30; confirms our solution : Make sense to you?

Age_Word_Problems/214165: 40 years ago i was 1/3 the age i will be in 4 years. How old am I? 1 solutions Answer 161755 by ankor@dixie-net.com(15638)   on 2009-09-16 15:23:24 (Show Source): You can put this solution on YOUR website! a = your age now ; 40 years ago i was 1/3 the age i will be in 4 years. a - 40 = (a+4) Multiply both sides by 3, to get rid of the annoying fraction 3a - 120 = a + 4 3a - a = 4 + 120 2a = 124 a = 62 yr is your age now ; : Check in the statement: 40 years ago i was 1/3 the age i will be in 4 years. 62 - 40 = (62 + 4) 22 = (66)

Divisibility_and_Prime_Numbers/214109: how would I be able to find numbers that are less than 300 and are divisible by 4 different prime numbers? 1 solutions Answer 161752 by ankor@dixie-net.com(15638)   on 2009-09-16 15:18:04 (Show Source): You can put this solution on YOUR website! how would I be able to find numbers that are less than 300 and are divisible by 4 different prime numbers? : there can't be many: 3 * 5 * 7 * 11 = 1155, a lot more than 300 : If you count 2 as a prime number 2 * 3 * 5 * 7 = 210, that would be the only one

Linear-systems/213787: sqrt(x+1)-sqrt(x-1)=2 1 solutions Answer 161748 by ankor@dixie-net.com(15638)   on 2009-09-16 15:10:31 (Show Source): You can put this solution on YOUR website! = 2 : Add to both sides = : Square both sides, FOIL the right side x + 1 = (x-1) + + 4 : x + 1 = x - 1 + 4 + : x + 1 = x + 3 + : x - x + 1 - 3 = : -2 = : Square both sides 4 = 16(x - 1) : 4 = 16x - 16 : 4 + 16 = 16x : 20 = 16x x = x = 1.25; however substitution in the original equation reveals this is not a solution. There is no solution

Numbers_Word_Problems/214070: Find the six-digit number in which the first digit is one less than the second digit and half the third; the fourth digit is one more than the third and is also the sum of the first and second digits; and the fifth and sixth digits make a number that is the sum of the first four digits. The sum of all the digits is 19. 1 solutions Answer 161746 by ankor@dixie-net.com(15638)   on 2009-09-16 14:45:14 (Show Source): You can put this solution on YOUR website! Write an equation for each statement : Find the six-digit number u, v, w, x, y, z : in which the first digit is one less than the second digit u = v-1 : and half the third; u = .5w : the fourth digit is one more than the third x = w+1 : and is also the sum of the first and second digits; x = u + v : the fifth and sixth digits make a number that is the sum of the first four digits. 10y + z = u + v + w + x : The sum of all the digits is 19. u + v + w + x + y + z = 19 : We can replace the 1st 4 digits with 10y + z 10y + z + y + z = 19 11y + 2z = 19 : From this we can write an equation that has only one positive integer solution 2z = 19-11y z = y = 1 z = z = z = 4 : u + v + w + x + y + z = 19 Replace y and z u + v + w + x + 1 + 4 = 19 u + v + w + x = 19 - 5 u + v + w + x = 14 : Replace u with .5w, replace x with w+1 .5w + v + w + (w+1) = 14 2.5w + v = 14 - 1 2.5w + v = 13 : We know that u = v-1 and we know that u = .5w, therefore .5w = v - 1 or v = .5w + 1 Replace v with (.5w+1) 2.5w + .5w + 1 = 13 3w = 13 - 1 3w = 12 w = 4 : Find v v = .5(4) + 1 v = 3 : So far we have: v=3, w=4, y=1, z=4 find x x = w+1 x = 4+1 x = 5 : find u u = .5w u = .5(4) u = 2 : The number: 234514 : Check this: 2 + 3 + 4 + 5 + 1 + 4 = 19

Travel_Word_Problems/214124: It's 56 miles to work, it takes 10 minutes longer to get to work than coming home, and you travel 8 mph faster coming home. What is your avg. speed coming home? 1 solutions Answer 161737 by ankor@dixie-net.com(15638)   on 2009-09-16 13:59:02 (Show Source): You can put this solution on YOUR website! It's 56 miles to work, it takes 10 minutes longer to get to work than coming home, and you travel 8 mph faster coming home. What is your avg. speed coming home? : Let s = speed coming home then (s-8) = speed going to work : Convert 10 min to hr : Write a time equation: Time = dist/speed : Time from work + 10 min = time to work + = Multiply equation by 6s(s-8), results: 56*6*(s-8) + s(s-8) = 6s*56 ; 336(s-8) + s^2 - 8s = 336s : 336s - 2688 + s^2 - 8s - 336s = 0 : Arrange as a quadratic equation s^2 - 8s - 2688 = 0 Factor to (s-56)(s+48) = 0 positive solution s = 56 mph on the return home : : Check solution (speed to work = 48 mph) 56/56 + 1/6 = 56/48 1 + .167 = 1.167

Graphs/214069: Hi, I am having a hard time figuring what formula or equation needs to be applied to this problem. There's a slope graph. (0,96) (2.5,196) Not sure if this is considered quadratic or just a simple word problem that need to be converted into an equation. The graph below shows the height in feet, of a ball thrown straight up with an initial speed of 80 feet per second from an initial height of 96 feet after t seconds. Use the graph to answer the following questions. a) What is the height of the ball at 1.5 seconds? b) What is the maximum height of the ball and at what time does it occur? c) Find the H intercept of the graph and explain what is happening to the ball at that point. d) Find the T intercept of the graph and explain what is happening to the ball at that point. 1 solutions Answer 161705 by ankor@dixie-net.com(15638)   on 2009-09-16 10:32:13 (Show Source): You can put this solution on YOUR website! The graph below shows the height in feet, of a ball thrown straight up with an initial speed of 80 feet per second from an initial height of 96 feet after t seconds. Use the graph to answer the following questions. : Perhaps we can construct the graph from the equation: h = -16t^2 + 80t + 96 -16t^2 is the downward pull of gravity 80t is the upward velocity of the ball 96 is initial height : : a) What is the height of the ball at 1.5 seconds? The graph indicates it to be about 180 ft : b) What is the maximum height of the ball and at what time does it occur? Looks like this occurs at 2.5 sec when the ball is at 196 ft : c) Find the H intercept of the graph and explain what is happening to the ball at that point. H intercept is on the y axis, occurs when x = 0, that would be 96 ft : d) Find the T intercept of the graph and explain what is happening to the ball at that point. T is on the x axis, intercept when y = 0, looks like at 6 secs when it hits the ground : it is a quadratic equation

Travel_Word_Problems/213913: Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southbound plane. After 4 hours the planes are 3080 miles apart. Find the speed of each plane. (Use 1 decimal place.) 1 solutions Answer 161656 by ankor@dixie-net.com(15638)   on 2009-09-15 22:00:55 (Show Source): You can put this solution on YOUR website! Two planes leave simultaneously from the same airport, one flying due east and the other due south. The eastbound plane is flying 100 miles per hour faster than the southbound plane. After 4 hours the planes are 3080 miles apart. Find the speed of each plane. (Use 1 decimal place.) : The distance between the planes is the hypotenuse of a right triangle a^2 + b^2 = c^2 : Let s = speed of the southbound plane then (s+100) = speed of the eastbound : Dist = speed * time : a = 4s; south distance b = 4(s+100); east distance c = 3080; distance between the planes after 4 hrs : (4s)^2 + (4(s+100))^2 = 3080^2 : 16s^2 + (4s+400)^2 = 9486400 : 16s^2 + (4s+400)^2 = 9486400 : 16s^2 + 16s^2 + 3200s + 160000 = 948640 ; 16s^2 + 16s^2 + 3200s + 160000 - 9486400 = 0 ; 32s^2 + 3200s - 9326400 = 0 : Simplify divide by 32: s^2 + 100s - 291450 = 0 : Using the quadratic formula; a=1; b=100; c=291450 ; I got a positive solution of 492.2 mph the south bound plane : then 592.2 mph the east bound plane ; : Check solution on a calc; enter = 3080

Proportions/213924: I am taking GED classes. We do not have a textbook just work sheets. 1. if 3 cans of asparagus cost $7.00, How much do 12 cans cost? 2. if it takes a basket maker 20 days to make 30 baskets, how many baskets can be made in 60 days? 1 solutions Answer 161590 by ankor@dixie-net.com(15638)   on 2009-09-15 19:27:18 (Show Source): You can put this solution on YOUR website! 1. if 3 cans of asparagus cost $7.00, How much do 12 cans cost? A ratio equation is one way: = Cross multiply 3x = 7*12 3x = 84 x = x = $28 for 12 cans : : 2. if it takes a basket maker 20 days to make 30 baskets, how many baskets can be made in 60 days? = 20x = 60*30 20x = 1800 x = x = 90 baskets in 60 days

Travel_Word_Problems/213850: Bryan took a 4-mile walk. The second half of his walk he averaged 1 mile per hour less than the first half, and it took him 1/3 hour longer. What rate did he average on the first half of the walk? This question has confused me and i do not know how to set it up. I know the total distance is 4 miles. He averaged 1/3 hour more on the second half. He walked 1 mile per hour less 1 solutions Answer 161578 by ankor@dixie-net.com(15638)   on 2009-09-15 19:06:59 (Show Source): You can put this solution on YOUR website! Bryan took a 4-mile walk. The second half of his walk he averaged 1 mile per hour less than the first half, and it took him 1/3 hour longer. What rate did he average on the first half of the walk? : Let s = speed on the 1st 2 mi then (s-1) = speed on the last 2 mi : Write a time equation: Time = 1st half time + 1/3 hr = 2nd half time + = Multiply equation by 3s(s-1) 3(s-1)*2 + s(s-1) = 3s(2) : 6s - 6 + s^2 - s = 6s : s^2 - s + 6s - 6s - 6 = 0 : s^2 - s - 6 = 0 Factor (s-3)(s+2) = 0 Positive solution s = 3 mph speed on the 1st half : : Check by finding the times 2/3 hr 2/2 - 1 hr; 1/3 hr difference

Finance/213866: solve A=P+Prt for P, given that A=$1120, r=10%, and t=6 years 1 solutions Answer 161554 by ankor@dixie-net.com(15638)   on 2009-09-15 17:10:43 (Show Source): You can put this solution on YOUR website! solve A=P+Prt for P, given that A=$1120, r=10%, and t=6 years : P + Prt = 1120 P + P*.10*6 = 1120 P + .6P = 1120 1.6P = 1120 P = P = $700 ; : Is this true: 700 + (700*.1*6) = 1120

Matrices-and-determiminant/213861: This question is from textbook Algebra 2 A jeweler plans to combine two silver alloys to make 50 grams of alloy that is 75% silver and contains 37.5 grams of pure silver (75% of 50 grams). If some silver alloy is 80% silver and the other is 60% silver, how many grams of each are needed? 1 solutions Answer 161552 by ankor@dixie-net.com(15638)   on 2009-09-15 16:47:47 (Show Source): You can put this solution on YOUR website! A jeweler plans to combine two silver alloys to make 50 grams of alloy that is 75% silver and contains 37.5 grams of pure silver (75% of 50 grams). If some silver alloy is 80% silver and the other is 60% silver, how many grams of each are needed? : Let x = amt of 80% silver required Resulting amt is to be 50, therefore: (50-x) = amt of 60% silver : .8x + .6(50-x) = .75(50) : .8x + 30 - .6x = 37.5 : .8x - .6x = 37.5 - 30 : .2x = 7.5 : x = x = 37.5 gr of 80% silver and 50 - 37.5 = 12.5 gr of 60% silver : Check solutions in the amt of silver equation .8(37.5) + .6(12.5) = .75(50) 30 + 7.5 = 37.5

Travel_Word_Problems/213855: The captain of the Titanic was warned of ice ahead, but he thought his ship was unsinkable, and continued his pace of 60 feet every 1.5 seconds. How fast was he traveling in miles per hour? How fast was he traveling in nauts per hour? 1 solutions Answer 161543 by ankor@dixie-net.com(15638)   on 2009-09-15 16:08:02 (Show Source): You can put this solution on YOUR website! pace of 60 feet every 1.5 seconds. How fast was he traveling in miles per hour? : = 27.27 mph : How fast was he traveling in nauts per hour? = 24 knots

Mixture_Word_Problems/213844: Ellen takes 1/4 of the oranges in a bowl Jeff takes 1/3 of the remaining oranges in the bowl. Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl. Carlos takes 1/2 of the oranges that remain in the bowl There are now 4 oranges left in the bowl. How many oranges were originally in the bowl? 1 solutions Answer 161537 by ankor@dixie-net.com(15638)   on 2009-09-15 15:55:28 (Show Source): You can put this solution on YOUR website! Ellen takes 1/4 of the oranges in a bowl Jeff takes 1/3 of the remaining oranges in the bowl. Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl. Carlos takes 1/2 of the oranges that remain in the bowl. There are now 4 oranges left in the bowl. How many oranges were originally in the bowl? ; Let x = amt originally in the bowl : "Ellen takes 1/4 of the oranges in a bowl" x - x = x remaining ; Jeff takes 1/3 of the remaining oranges in the bowl. that means he leaves 2/3 * x = x x reduces to x remaining : Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl. x + 2 : Carlos takes 1/2 of the oranges that remain in the bowl There are now 4 oranges left in the bowl. (x + 2) = 4 multiply both sides by 2 x + 2 = 8 x = 8 - 2 x = 6 multiply both sides by 2 x = 2(6) x = 12 oranges originally : : Check solution: Ellen takes 1/4 of the oranges in a bowl 1/4 of 12 = 3, leaving 9 Jeff takes 1/3 of the remaining oranges in the bowl. 1/3 of 9 = 3. leaving 6 Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl. 6 + 2 = 8 Carlos takes 1/2 of the oranges that remain in the bowl. half of 8 = 4

Proportions/213793: an adult sets out from home to pick up their child from school, and walks at a pace that will take 10 minutes to get to the school. At exactly the same time,the child leaves school to walk home at a pace that will take 20 minutes to get home. After how long will they meet? How would you justify your solution to the child? 1 solutions Answer 161529 by ankor@dixie-net.com(15638)   on 2009-09-15 15:22:42 (Show Source): You can put this solution on YOUR website! an adult sets out from home to pick up their child from school, and walks at a pace that will take 10 minutes to get to the school. At exactly the same time,the child leaves school to walk home at a pace that will take 20 minutes to get home. After how long will they meet? ; Let t = time interval when they walk towards each other : From the information given, we can say the adult walks twice as fast as the child Let s = walking speed of the child then 2s = walking speed of the adult and 3s = their relative speed walking towards each other : Write a dist equation Dist = speed * time : Combined dist = child walking 20 min to home 3s(t) = 20s divide both sides by s 3t = 20 t = t = 6 min or Combined dist = adult walking 10 min 3s(t) = 10(2s) 3s(t) = 20t divide both sides by s 3t = 20 t = t = 6 min : How would you justify your solution to the child? : You can say since I walk twice as fast as you do, I will cover twice the distance. therefore in 6 min, child covers the dist and in 6 min, adult covers the dist (twice as fast)

Rectangles/213483: Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer than the width. The larger rectangle has 6 more square feet than the smaller. What is the width of the rectangles? 1 solutions Answer 161436 by ankor@dixie-net.com(15638)   on 2009-09-14 21:59:03 (Show Source): You can put this solution on YOUR website! Two rectangles have the same width. let w = width of both rectangles : The length of one is 1 foot longer than the width. L1 = w + 1 The length of the other is 2 feet longer than the width. L2 = w + 2 ; The larger rectangle has 6 more square feet than the smaller. W*L2 - W*L1 = 6 : What is the width of the rectangles? Replace L2 in the above equation with (W+2); Replace L1 in the above equation with ((W+1) W*(W+2) - W*(W+1) = 6 W^2 + 2W - W^2 - W = 6 2W - W = 6 W = 6 is the width of both rectangles ; : Check solution 8*6 - 7*6 = 6

Equations/213630: The speed limit on a certain highway is 72km/h. What is this speed in cm/s? 1 solutions Answer 161431 by ankor@dixie-net.com(15638)   on 2009-09-14 21:47:44 (Show Source): You can put this solution on YOUR website! The speed limit on a certain highway is 72km/h. What is this speed in cm/s? : = 2000 cm/sec

Quadratic_Equations/213547: A college student has finished 49 credit hours with a GPA of 2.5. To get into the program she wishes to enter, she must have a GPA of 3.3. How many additional credit hours of 4.0 work will raise her GPA to 3.3? 1 solutions Answer 161380 by ankor@dixie-net.com(15638)   on 2009-09-14 19:05:30 (Show Source): You can put this solution on YOUR website! A college student has finished 49 credit hours with a GPA of 2.5. To get into the program she wishes to enter, she must have a GPA of 3.3. How many additional credit hours of 4.0 work will raise her GPA to 3.3? : Let x = no. of 4.0 credits required : = 3.3 = 3.3 Multiply both sides by (x+49) 4x + 122.5 = 3.3(x+49) : 4x + 122.5 = 3.3x + 161.7 : 4x - 3.3x = 161.7 - 122.6 : .7x = 39.1 x = x = 55.857 ~ 56 additional 4.0 credit hrs, to get a 3.3 gpa (sounds almost impossible!) : : Check: final total credit hr 49 + 56 = 105 = = = 3.3

Rectangles/213554: A farmer wants to make a rectangular enclosure along the side of a barn and then divide the enclosure into two pens with a fence constructed at a right angle to the barn. If 300 yards of fencing are available, what are the dimensions of the largest section that can be enclosed? Firstly, the wording of this particular problem has thrown both myself, family, and friends for a loop. I have drawn, erased, and redrawn several rough sketches of this barn-and-fence problem and still feel as though it is wrong. I am at a loss of going about how to solve it. Any assistance would be greatly appreciated! Thank you in advance -B 1 solutions Answer 161342 by ankor@dixie-net.com(15638)   on 2009-09-14 17:20:48 (Show Source): You can put this solution on YOUR website! A farmer wants to make a rectangular enclosure along the side of a barn and then divide the enclosure into two pens with a fence constructed at a right angle to the barn. If 300 yards of fencing are available, what are the dimensions of the largest section that can be enclosed? : _________________Barn |_____|_____| : I think it looks something like this: Then we can write an equation for the 300 yds of fencing L + 3W = 300 : L = (300-3W) : Area = L*W Replace L with (300-3W) A = (300-3W) * W Arrange as a quadratic equation A = -3W^2 + 300W Find the axis of symmetry for Width that gives max area x = -b/(2a) in this equation a=-3; b=300 W = -300/(2*-3) W = -300/-6 W = +50 ft is the width for max area : Find the length L = 300 - 3(50) L = 150 ft is the length : Max area would be 150 * 50 = 7500 sq/ft

Money_Word_Problems/213507: This question is from textbook The revenue for selling x units of the product is R=115.95x. The cost of producing x units is C=95x+750. To obtain a profit, the revenue must be greater than the cost. For what values of x will this product return a profit. 1 solutions Answer 161298 by ankor@dixie-net.com(15638)   on 2009-09-14 15:09:31 (Show Source): You can put this solution on YOUR website! The revenue for selling x units of the product is R=115.95x. The cost of producing x units is C=95x+750. To obtain a profit, the revenue must be greater than the cost. For what values of x will this product return a profit. : R > C 115.95x > 95x + 750 Subtract 95x from both sides 115.95 - 95x > 750 20.95x > 750 divide both sides by 20.95 x > x > 35.8 units Have to sell at least 36 units to make a profit ; : Check in the original equation 115.95(36) > 95(36) + 750 4174.20 > 3420 + 750 4174.20 > 4170; a slight profit of $4.20

Linear-equations/213427: This question is from textbook PRECALCULUS WHAT TYPE OF FORMULA AM I SUPPOSE TO USE IN ORDER TO FIND THE VALUE OF X 0R Y. THE DIRECTIONS SAY, "FIND THE VALUE OF X OR Y SO THAT THE LINE THROUGH THE PAIR OF POINTS HAS THE GIVEN SLOPE." I'M NOT SURE HOW TO DO THAT. THE GIVEN IS (-2,3) AND (4,y) with the slope of -3. 1 solutions Answer 161206 by ankor@dixie-net.com(15638)   on 2009-09-14 08:01:31 (Show Source): You can put this solution on YOUR website! WHAT TYPE OF FORMULA AM I SUPPOSE TO USE IN ORDER TO FIND THE VALUE OF X 0R Y. THE DIRECTIONS SAY, "FIND THE VALUE OF X OR Y SO THAT THE LINE THROUGH THE PAIR OF POINTS HAS THE GIVEN SLOPE." I'M NOT SURE HOW TO DO THAT. THE GIVEN IS (-2,3) AND (4,y) with the slope of -3. : Use the slope formula to find y: that is = m Assign the given values as follows: x1=-2; y1=3 x2 =4; y2= y m = -3 : Substitute the given values as follows and find y = -3 = -3 = -3 Multiply both sides by 6 y - 3 = 6(-3) y = -18 + 3 y = -15; the pair is: 4,-15 ; Use the point/slope formula to find the equation y - y1 = m(x - x1) Substitute the given values y - 3 = -3(x -(-2)) y - 3 = -3(x + 2) y - 3 = -3x - 6 y = -3x - 6 + 3 y = -3x - 3 is the equation : Check solution by substituting the x value of 4 y = -3(4) - 3 y = = -12 - 3 y = -15 which is the value we got for y

Angles/213212: This is a question from a worksheet... One of two copmlemtentary angles added to one-half of the other yields 72degrees. Find the half the measure of the larger. not quite sure how to work the problem........thank you for your time! i really appreciate it! 1 solutions Answer 161091 by ankor@dixie-net.com(15638)   on 2009-09-13 16:39:30 (Show Source): You can put this solution on YOUR website! One of two complemtentary angles added to one-half of the other yields 72degrees. Find the half the measure of the larger. : the two angles: x and (90-x) : x + .5(90-x) = 72 x + 45 - .5x = 72 x - .5x = 72 - 45 .5x = 27 Multi both sides by 2 x = 54 degrees, has to be the larger : .5(54) = 27 degrees

Linear_Equations_And_Systems_Word_Problems/213169: This question is from textbook Prentice Hall Algebra I Louisiana A moving van leaves a house traveling at an average rate of 35mph. The family leaves the house in a car 3/4 hour later traveling the same route at an average rate of 50mph. How long will it take the family to catch up with the van? 1 solutions Answer 161056 by ankor@dixie-net.com(15638)   on 2009-09-13 12:29:15 (Show Source): You can put this solution on YOUR website! A moving van leaves a house traveling at an average rate of 35mph. The family leaves the house in a car 3/4 hour later traveling the same route at an average rate of 50mph. How long will it take the family to catch up with the van? : Change 3/4 hr to .75 hr : Let t = time required by the family to catch up then (t+.75) = Van travel time when it is caught : When this happens, they will have traveled the same distance Write a distance equation: dis = speed * time : Car dist = Van dist 50t = 35(t+.75) 50t = 35t + 26.25 50t - 35t = 26.25 15t = 26.25 t = t = 1.75 hrs for the family to catch the van ; : Check solution by ensuring that they traveled the same dist: 50 * 1.75 = 87.5 mi 35 * (1.75+.75) = 87.5

Rate-of-work-word-problems/213071: allan can finish a set of furniture in 8 days. ben can finish the same set of furniture in 6 days. if allan starts working for 2 days, and then ben joined him, in how many days will the set of furniture be finished by the two men? 1 solutions Answer 160965 by ankor@dixie-net.com(15638)   on 2009-09-12 22:02:08 (Show Source): You can put this solution on YOUR website! allan can finish a set of furniture in 8 days. ben can finish the same set of furniture in 6 days. if allan starts working for 2 days, and then ben joined him, in how many days will the set of furniture be finished by the two men? : let t = time working together : Let the completed job = 1 : + = 1 Multiply equation by 24, results 3(t+2) + 4t = 24 3t + 6 + 4t = 24 3t + 4t = 24 - 6 7t = 18 t = t = 2.57 days working together ; : Check + = .57 + .43 = 1

Age_Word_Problems/213069: Ricky is 26 yrs old and Jenny is 5 yrs old. in how many yrs will ricky be twice as old as jenny? 1 solutions Answer 160964 by ankor@dixie-net.com(15638)   on 2009-09-12 21:52:22 (Show Source): You can put this solution on YOUR website! : Ricky is 26 yrs old and Jenny is 5 yrs old. in how many yrs will ricky be twice as old as jenny? : Let t = no. of yrs for this to be true : 26 + t = 2(5+t) 26 + t = 10 + 2t 26 - 10 = 2t - t 16 = t ; : Check: 26 + 16 = 2(5 + 16) 42 = 2(21)

Angles/212961: This question is from textbook Geometry for Enjoyment and Challenge I have a picture with segment XY is perpendicular to segment YW. Ray YZ forms two angles within the 90 degrees of angle XYW. these ar identified as angle x (angle XYZ) and angle y (angle ZYW). The next picture i have has segment AB is perpendicular to segment BC. A segment BD is within this 90 degrees showing angles (2x)degrees (angle ABD) and (y-50) degrees (angle DBC). I need to find the measure of angle DBC. I used two equations and two unknowns and came up with x =50 degrees and y = 40 degrees. that doesn't work when i use y=40 in the second picture with the angle DBC = (y-50)degrees. This would make that angle a negative number. 1 solutions Answer 160960 by ankor@dixie-net.com(15638)   on 2009-09-12 21:09:43 (Show Source): You can put this solution on YOUR website! I have a picture with segment XY is perpendicular to segment YW. Ray YZ forms two angles within the 90 degrees of angle XYW. these ar identified as angle x (angle XYZ) and angle y (angle ZYW). The next picture i have has segment AB is perpendicular to segment BC. A segment BD is within this 90 degrees showing angles (2x)degrees (angle ABD) and (y-50) degrees (angle DBC). I need to find the measure of angle DBC. I used two equations and two unknowns and came up with x =50 degrees and y = 40 degrees. that doesn't work when i use y=40 in the second picture with the angle DBC = (y-50)degrees. This would make that angle a negative number. : That's true but that has to be the answer, if x=50 then ABD = 100 then DBC has to be 40 - 50 = -10: 100 - 10 = 90 degrees. I think you did it right!

Surface-area/213062: Henry is ten more than two times as old as Cheryl. In 20 years the sum of their ages will be 92. How old is Cheryl now? 1 solutions Answer 160953 by ankor@dixie-net.com(15638)   on 2009-09-12 20:26:01 (Show Source): You can put this solution on YOUR website! Let h = Henry's present age Let c = Cheryl's present age ; Write an equation for each statement: : Henry is ten more than two times as old as Cheryl. h = 2c + 10 : In 20 years the sum of their ages will be 92. (h+20) + (c+20) = 92 h + c + 40 = 92 h + c = 92 - 40 h + c = 52 : How old is Cheryl now? : Replace h with (2c+10) 2c + 10 + c = 52 2c + c = 52 - 10 3c = 42 c = c = 14 yrs is Cheryl's present age ; : Check solution: Find h: h + 14 = 52; h = 38 Check solution in the statement: "In 20 years the sum of their ages will be 92." 38 + 20 + 14 + 20 = 92

Rectangles/213061: The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 100 centimeters squared, what is the length of the diagonal? So far i have this: W= 2L-9 L= ? L(2L-9)=100 2L^2-9L-100=0 I tried to factor it and used the quadratic formula and I still couldn't get answer. Please help. Thank you! 1 solutions Answer 160951 by ankor@dixie-net.com(15638)   on 2009-09-12 20:11:30 (Show Source): You can put this solution on YOUR website! : Find the diagonal d = d = 14.157 is the diagonal

Proportions/213023: by weight, the ratio of chlorine to sodium in table salt is 35.46 to 23.00. How much sodium is contained in 50.00kg or salt? Has to be set up as an appropriate proportion and then be solved. 1 solutions Answer 160944 by ankor@dixie-net.com(15638)   on 2009-09-12 19:30:07 (Show Source): You can put this solution on YOUR website! by weight, the ratio of chlorine to sodium in table salt is 35.46 to 23.00. How much sodium is contained in 50.00kg or salt? Has to be set up as an appropriate proportion and then be solved. : Let x = amt of sodium in 50 kg then (50-x) = amt of chlorine in 50 kg ; A ratio equation: = cross multiply 35.46x = 23(50-x) 35.46x = 1150 - 23x 35.46x + 23x = 1150 58.46x = 1150 x = x = 19.67 kg of sodium ; : check: Chlorine: 50 - 19.67 = 30.33 : 23/35.46 = .6486 19.67/30.33 = .6485; close enough

Exponential-and-logarithmic-functions/213021: I'ts been a while since I've solved these kinds of questions (ok 20+ years!) so I need a refresher. I looked a similar problems on-line, but am struggling with how to set it up. Here's the problem: Sam invested $5000 for one year, part at 9% annual interest and the rest at 12% annual interest. The interest from the investment at 9% was $198 more than the interest from the investment at 12%. How much money did she invest at 9%? 1 solutions Answer 160918 by ankor@dixie-net.com(15638)   on 2009-09-12 16:58:39 (Show Source): You can put this solution on YOUR website! Sam invested $5000 for one year, part at 9% annual interest and the rest at 12% annual interest. The interest from the investment at 9% was $198 more than the interest from the investment at 12%. How much money did she invest at 9%? : Let x = amt invested at %9 Total invested given as 5000, therefore (5000-x) = amt invested at 12% : .09x - 298 = .12(5000-x) .09x - 298 = 600 - .12x .09x + .12x = 600 + 298 .21x = 898 x = x = $4,276.19 invested at 9% then 5000 - 4276.19 = $723.08 invested at %12 : : Is this true? find the interest of each .09*4276.19 = 384.86 .12 * 723.08 = 86.86 ------------------- difference = 298; confirms these solutions

Travel_Word_Problems/212983: This question is from textbook Physics a world view At an average speed of 11 m/s, how many kilometers can a cyclist travel in a 6 hour day? 1 km 1 solutions Answer 160896 by ankor@dixie-net.com(15638)   on 2009-09-12 14:17:28 (Show Source): You can put this solution on YOUR website! At an average speed of 11 m/s, how many kilometers can a cyclist travel in a 6 hour day? : 1 hr = 3600 sec : d = d = 237.6 km in 6 hrs