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 test/697782: On Wednesday there were no tandem bikes for sale. There were only bicycles and tricycles in the shop. There are a total of 24 seats and 61 wheels in the shop. How many are bicycles and how many are tricycles?1 solutions Answer 430276 by josmiceli(9649)   on 2013-01-01 21:01:20 (Show Source): You can put this solution on YOUR website!Let = number of bicycles Let = number of tricycles Both types have 1 seat each, so (1) and (2) ------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and (1) (1) (1) There are 11 bicycles and 13 tricycles check answer: (2) (2) (2) (2) OK
 Money_Word_Problems/697716: Trying to help myself and my 11 yr old daughter understand these word problems. Joseph, Brian, and Kyle spent \$1,189 to buy a pc for their dad. Brian paid \$148 more than Joe. Joe paid \$399 less than Kyle. How much did Brian pay? Your help will be greatly appreciated...1 solutions Answer 430240 by josmiceli(9649)   on 2013-01-01 16:34:57 (Show Source): You can put this solution on YOUR website!I always assign letters to the unknowns fight away Let = amount in dollars that Joseph paid Let = amount in dollars that Brian paid Let = amount in dollars that Kyle paid -------------------------------------- given: (1) (2) (3) ----------------- Substitute (2) into (1) (1) and (3) (3) Substitute (3) into (1) (1) (1) (1) (1) and, since (2) (2) (2) and (3) (3) (3) Brian paid \$362 check: (1) (1) (1) OK
 Rate-of-work-word-problems/697659: Hi, two rats eat 2 pieces of cheese in 2 minutes, how many rats will eat 6 pieces in 6 minutes, kindly advise. regards1 solutions Answer 430220 by josmiceli(9649)   on 2013-01-01 14:56:40 (Show Source): You can put this solution on YOUR website!This is a rate problem, just like the rate problems about pipes filling swimming pools, etc. ------------ It is assumed here that rats always eat at the same rate 2 rats eat 2 pieces in 2 min ----------------------- 3 times as many rats will eat 3 times as many pieces in the same amount of time, so 6 rats eat 6 pieces in 2 min ----------------------- 1/3 as many rats will eat the same number of pieces in 3 times that time, so 2 rats eat 6 pieces in 6 min ----------------------- Another way you can look at it is: Give 2 rats 2 pieces, and wait until they finish Then give them 2 more pieces- wait until they finish Give them 2 more pieces Each time, they take 2 min, thats 6 min for 6 pieces
 Mixture_Word_Problems/697694: A nut shop sells almonds for \$1.80 a pound, walnuts for \$1.30, and peanuts for \$.65 a pound. the shopkeeper makes a mixture of 21 pounds of these nuts to sell for \$1.00 a pound. he used twice as many pounds of peanuts as walnuts. how much of each kind of nut did he use?1 solutions Answer 430216 by josmiceli(9649)   on 2013-01-01 14:40:28 (Show Source): You can put this solution on YOUR website!Let = pounds of almonds needed Let = pounds of walnuts needed Let = pounds of peanuts needed given: (1) (2) ( the is \$1/pound ) (3) ------------- This is 3 equations with 3 unknowns, so it's solvable (2) (2) (2) ---------------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) Substitute this result and (3) into (1) (1) (1) (1) (1) (1) (1) and, since (3) (3) (3) and (1) (1) (1) (1) 3 pounds of almonds are needed 6 pounds of walnuts are needed 12 pounds of peanuts are needed check answer: (2) (2) (2) (2) OK
 Travel_Word_Problems/697683: the distance between alicas house and paquias house is 1600 feet, if it takes alicias 3 seconds to walk 10 feet, how long will it take her to walk to paquitas house?1 solutions Answer 430211 by josmiceli(9649)   on 2013-01-01 14:17:04 (Show Source): You can put this solution on YOUR website!Her rate of walking is ft/sec Multiply both sides by sec and, since there are sec/min It takes her 8 min to get there
 Mixture_Word_Problems/697685: How much pure rubbing alcohol must be added to 20kg of a 12% alcohol solution to give you a 32% ALCOHOL SOLUTION?1 solutions Answer 430209 by josmiceli(9649)   on 2013-01-01 13:52:36 (Show Source): You can put this solution on YOUR website! kg of pure rubbing alcohol in 12% solution Let = kg of pure rubbing alcohol to be added 5.882 kg of pure rubbing alcohol must be added check answer: OK
 test/697679: Please help me with this problem.I don't understand it. My teacher never went over these kinds of problems in class. I would really appreciate it if you would explain and answer. A farmer has 526 meters of fencing available to enclose a rectangular portion of his land. One side of the rectangle being fenced lies along a river, so only three sides require fencing. (a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river. (b) For what value of x is the area largest? Thanks in advance!1 solutions Answer 430207 by josmiceli(9649)   on 2013-01-01 13:43:19 (Show Source): You can put this solution on YOUR website! is the length of the side parallel to the river. Each of the sides that are perpendicular to the river are Let = area of enclosed portion This is a parabola which has a maximum because the coefficient of the term is negative and the term is positive. The maximum is at when the equation has the form 263 meters answer This is the x-co-ordinate of the maximum area, which is the length of fencing parallel to the river. ------------- If you want the maximum Area, just plug this back into the equation m2 ------------------------ It's easy to test this result. if is slightly more than or less than , the area should go down slightly also If I say , then It went down You can check for The area should also go down by roughly the same amount.
 test/697627: A man is 37 years old and his child's age is 8. How many years ago was the product of their ages 961 solutions Answer 430179 by josmiceli(9649)   on 2013-01-01 06:21:54 (Show Source): You can put this solution on YOUR website!Let = that number of years given: Use quadratic formula and also, It could not have been 40 yrs ago- The man wasn't born yet. It must have been 5 years ago check the answer: OK
 Linear-systems/697626: Please help me solve this equation: A risograph machine can finish 100 pages in 1 minute. How many books of 250 pages can the machine copy in 20 minutes ? 1 solutions Answer 430178 by josmiceli(9649)   on 2013-01-01 06:04:04 (Show Source): You can put this solution on YOUR website!Let = number of books of pages that the machine can copy in min Note that would be the number of pages that the machine can copy in min -------------- The machine's rate of copying is pages / min I can say that This is just ( pages/min = pages/min ) The machine can copy 8 books of 250 pages in 20 min check: OK
 Complex_Numbers/697544: In 5 min a conveyor belt moves 400 pounds of cans to a storage area. A smaller belt moves the same quantity of cans the same distance in 9 minutes. How long does it take if belts are used 1 solutions Answer 430177 by josmiceli(9649)   on 2013-01-01 05:49:40 (Show Source): You can put this solution on YOUR website!Add their rates of moving cans to get their rate moving them together. 1st belt: Rate = ( 400 lbs of cans ) / ( 5 min ) 2nd belt: Rate = ( 400 lbs of cans ) / ( 9 min ) ------------------------------- Let = time in minutes to move 400 cans with both belts used Call 400 cans " 1 job " Multiply both sides by min Both belts can move 400 cans in 3.2143 min check: OK- error due to rounding off
 percentage/697614: out of 880000 i invested 545000 how much percent is 545000 of 8800001 solutions Answer 430176 by josmiceli(9649)   on 2013-01-01 05:39:01 (Show Source): You can put this solution on YOUR website!Per cent means "per one-hundred" so I can say Multiply both sides by 545000 is 61.932% of 880000 check answer: 61.932% = The error is due to rounding off
 Age_Word_Problems/697611: Author is 10 years older than Carol. 9 years ago his age was 3 times her age. How old will they each be in 4 years?1 solutions Answer 430175 by josmiceli(9649)   on 2013-01-01 05:29:49 (Show Source): You can put this solution on YOUR website!Let = Arthur's age now Let = Carol's age now given: (1) (2) ----------------------- (2) (2) and (1) ------------------ Subtract (2) from (1) (1) (2) and (1) (1) (1) -------------- In 4 years Arthur will be 24 In 4 years Carol will be 18 ---------------------- check: (2) (2) (2) (2) OK
 Linear_Equations_And_Systems_Word_Problems/697623: please help me solve this : a man left an amount of \$525,000 to be divided among his widow, two sons and one daughter, each son was to receive twice the amount the daughter would receive, and the widow was to have eight times the amount each son would receive. how much was the widows share?1 solutions Answer 430174 by josmiceli(9649)   on 2013-01-01 05:18:48 (Show Source): You can put this solution on YOUR website!Let = the share for 1 son Let = the share for the daughter Let = the share for the widow given: (1) (2) (3) ------------- (2) Substitute this into (1) (1) and, also, substitute (3) into (1) (1) (1) (1) (1) and The widow's share is \$400,000 check: (2) (2) and (1) (1) (1) (1) OK
 Expressions-with-variables/697595: if a man walks for 20 minutes and then drives in his car for an hour and a half he goes a total distance of 46 miles. If he walks for 40 minutes and then drives for one hour and ten minutes, the speeds of walking and driving being the same as before, he travels 37 miles. Find his rates of walking and driving.1 solutions Answer 430140 by josmiceli(9649)   on 2012-12-31 17:32:18 (Show Source): You can put this solution on YOUR website!Let = his speed walking Let = his speed driving given: (1) miles (2) miles ------------ (1) (1) and (2) (2) --------------------- Multiply both sides of (1) by and subtract (2) from (1) (1) (2) and, since (1) (1) (1) (1) He walks 3 mi/hr and drives 30 mi/hr
 Points-lines-and-rays/697594: if i have a 16 inch diameter pizza cut into 6 slices what would the interior angle and arc length be of the slices?1 solutions Answer 430129 by josmiceli(9649)   on 2012-12-31 16:47:25 (Show Source): You can put this solution on YOUR website!The entire interior angle is 360 degrees The interior angle of each slice is 60 degrees The entire arc length is the circumference of the speaker. in An arc length of one of the slices is inches
 Miscellaneous_Word_Problems/697589: Three of Santa's helpers are a combined height of eleven feet and three inches. William is twelve inches shorter than Timothy, who is nine inches taller than James. How tall is each of Santa's helpers?1 solutions Answer 430124 by josmiceli(9649)   on 2012-12-31 16:32:07 (Show Source): You can put this solution on YOUR website!Let William's height = Let Timothy's height = Let James' height = given: (1) ( note that 3" is 1/4 of a foot ) (2) ( 12" is 1 foot ) (3) ( 9" is 3/4 of 1 foot ) ------------------ This is 3 equations and 3 unknowns, so it's solvable Substitute (2) into (1) (1) (1) and (3) (2) Substitute (2) into (1) (1) ( all units are in feet ) (1) (1) (1) and, since (2) (2) (2) (2) and (1) (1) (1) (1) (1) (1) -------------------- William is 10/3 ft, or 3 ft 4 in Timothy is 13/3 ft, or 4 ft 4 in James is 43/12 ft, or 3 ft 7 in ----------- Hope I got it
 Percentage-and-ratio-word-problems/697459: After a 20% price increase, the new price of a jacket is \$78. What was the jacket's original price? 1 solutions Answer 430035 by josmiceli(9649)   on 2012-12-30 21:07:58 (Show Source): You can put this solution on YOUR website!Let = the original price given: The original price was \$65
 test/697328: To beat at a rate of 200 beats per minute, a dragonfly's wing must be .36 inches. Using this data, find the constant for the inverse variation relating the length of an insect's wings to the beats per minute. B. Using the constant you found in A, state whether a dragonfly with a wingspan of 1.2 inches will be able to stay aloft if his wings beat 50 times per second. Using complete sentences, explain your answer. I really don't understand these two questions, your help will be highly appreciated!!! Thanks! 1 solutions Answer 430025 by josmiceli(9649)   on 2012-12-30 20:54:08 (Show Source): You can put this solution on YOUR website!They are basically saying that the dragonfly's wing will beat faster the shorter it is made. Let = speed of the wing in beats / min Let = the length of the wing in inches ---------- They are say ing that where is the constant of inverse variation. given: ---------- It sounds like the speed of the beating has to be the given minimum, or the dragonfly cannot fly. given: beats/sec beats/sec is slower that this, so the dragonfly will not stay aloft beating at this speed
 Linear_Equations_And_Systems_Word_Problems/697453: kiran sets off on a walk at a speed of 6km/h. 10 minutes later, her brother Ali sets off her on his bicycle at 15km/h. How far must Ali go to catch up with Kiran?1 solutions Answer 430023 by josmiceli(9649)   on 2012-12-30 20:40:37 (Show Source): You can put this solution on YOUR website!Start a stopwatch when Ali leaves. By then, Kiran has had a head start of hrs and a distance of km -------------- Let = the time in hrs on the stopwatch when Ali catches Kiran. Let = the distance in km that Ali travels in time . --------------- Kiran's equation: (1) Ali's equation: (2) ---------------- (1) Substitute (1) into (2) (2) (2) (2) (2) and (2) (2) (2) Ali must travel 1.667 km to catch Kiran check: (1) (1) (1) (1) (1) OK
 Miscellaneous_Word_Problems/697444: a carpenter needs to cut four sections each 3 feet 8 inches long from a piece of motor. if the bored is only sold by the foot what's the shortest length of bored she can buy1 solutions Answer 430015 by josmiceli(9649)   on 2012-12-30 20:10:56 (Show Source): You can put this solution on YOUR website!8 inches is ft 3 ft is ft This is more than 14 ft, so the shortest board that will work is 15 ft
 Money_Word_Problems/697434: A laptop computer is purchased for \$1200 . Each year, its value is 70% of its value the year before. After how many years will the laptop computer be worth \$300 or less? Write the answer as a whole number. 1 solutions Answer 429991 by josmiceli(9649)   on 2012-12-30 17:46:01 (Show Source): You can put this solution on YOUR website!For now, let = the purchase price The value is: 1st yr: 2nd yr: 3rd yr: 4th yr: etc Let = the current value of the laptop ------------------ If the number of years, ( I use the because it makes the 1st year ) Take the log base 10 of both sides After the 4th year, the laptop will be worth \$300 or less. ---------------- Check answer: OK
 Money_Word_Problems/697428: The monthly cost (in dollars) of water use (in dollars) is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 17 HCF of water is \$34.47 , and the cost for using 45 HCF is \$80.67 . What is the cost for using 25 HCF of water? 1 solutions Answer 429988 by josmiceli(9649)   on 2012-12-30 17:18:43 (Show Source): You can put this solution on YOUR website!Basically, they are giving you 2 points on a graph, and they want you to find a 3rd point. Plot hundreds of ft3 ( HFC ) on the horizontal axis and Monthly cost on the vertical axis. --------------- Given: ( 17, 34.47 ) and ( 45, 80.67 ) ------------ Let = Monthly cost of water use Let = HFC's of water ------------ Use the general point-slope formula answer ------------------- check answer: Does the line include ( 45, 80.67 ) OK- you can check ( 17, 34.47 ) ---------------------------- What is the cost for using 25 HCF of water? The cost is \$47.67
 Quadratic_Equations/697410: fareed earned rs.36000 by working a part time for 9 months and full time for 2 months.at the same monthly wages ghyas earned Rs.31200 by working part time for 10 months and full time for 1 month.find the monthly wages for each type of work. ? 1 solutions Answer 429963 by josmiceli(9649)   on 2012-12-30 14:12:08 (Show Source): You can put this solution on YOUR website!Let = part-time rate of pay Let = full-time rate of pay given: Fareed: (1) Ghyas: (2) ----------------------- Multiply both sides of (2) by and subtract (1) from (2) (2) (1) and, since (2) (2) (2) (2) ---------------- full-time wages are rs. 7200 /month part-time wages are rs. 2400 /month ------------------------- check: (1) (1) (1) (1) OK
 Money_Word_Problems/697408: Ivan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges an initial fee of \$40 and an additional .80 cents for every mile driven. Company B charges an initial fee of \$53 and an additional .60 cents for every mile driven. For what mileages will Company A charge less than Company B? Write your answer as an inequality, using m for the number of miles driven. 1 solutions Answer 429962 by josmiceli(9649)   on 2012-12-30 13:54:12 (Show Source): You can put this solution on YOUR website!First, I'll find the milage for which both companies charge the same Let = the charge for the day given: Company A: (1) Company B: (2) ------------------- Making the charges equal: ----------- So, for 65 miles driven, the charge is the same for both companies I want to know if A charges less than B with more miles driven or less miles driven. What If I say ? Company A: (1) (1) (1) (1) Company B: (2) (2) (2) (2) You can see that for slightly more than 65 miles driven, B charges less than A. That means less than 65 miles must be driven for A to charge less than B. answer
 Trigonometry-basics/697406: The perimeter of a rectangle is 24 feet. a. If x is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of x. b. If y is the area of the rectangle, express the area in terms of x.1 solutions Answer 429961 by josmiceli(9649)   on 2012-12-30 13:31:19 (Show Source): You can put this solution on YOUR website!(a) The formula for perimeter is: I'm calling one side and the adjacent side given: Subtract from both sides Divide both sides by The adjacent side is ft ----------------------------- (b) given: Area = The formula for area, using my variables, would be and, since
 Complex_Numbers/697387: What's the answer? (5-2i)(3+4i)1 solutions Answer 429954 by josmiceli(9649)   on 2012-12-30 11:03:03 (Show Source): You can put this solution on YOUR website! All you have to know here is that answer
 Length-and-distance/697381: the midpoint of "AB" is M. If the coordinates of A are (2,-6) and the coordinates of M are (5,-1) what are the coordinates of B?1 solutions Answer 429953 by josmiceli(9649)   on 2012-12-30 10:56:10 (Show Source): You can put this solution on YOUR website!You are looking for B( x,y ) which is an endpoint. The x-coordinate of the mid-point is defined as: (1) The y-coordinate of the mid-point is defined as: (2) ------------------------- ------------- Filling in the numbers: (1) (2) ------------------------- (1) (1) and (2) (2) ---------------- The coordinates of B are: B( 8,4 )
 Miscellaneous_Word_Problems/697318: Three years ago, Jerri was four times as old as Kelly was then. Five years from now, Jerri will be twice as old as Kelly will be. how old will each one be ten years from now?1 solutions Answer 429892 by josmiceli(9649)   on 2012-12-29 21:42:58 (Show Source): You can put this solution on YOUR website!Let = Jerri's age now Let = Kelly's age now = Jerri's age 3 years ago = Kelly's age 3 years ago = Jerri's age 5 years from now = Kelly's age 5 years from now ------------------------------------ given: (1) (2) ------------------------ (1) (1) and (2) (2) (2) ----------------- Subtract (1) from (2) (2) (1) and (2) (2) (2) (2) ------------- In 10 years, Jerri will be In 10 years Kelly will be ---------- check answers (1) (1) (1) (1) and (2) (2) (2) (2) OK
 Equations/697324: I do not understand at all Donald gave Louie a number of marbles to share with Dewey and Huey. Making sure that he got his share, Louie took one-third of the marbles and hid them. Dewey, after hearing from Donald that he is entitled to one-third of the marbles as well, went and hid one-third of the remaining marbles. Not knowing what was going on, Daisy took two marbles from the pile. When Huey came, there were only 10 marbles left. How many marbles did Donald give to Louie in the beginning? This is as far as I have gotten. x-1/3-(1/3)-21 solutions Answer 429884 by josmiceli(9649)   on 2012-12-29 21:27:33 (Show Source): You can put this solution on YOUR website!Let = the number of marbles that Donald gave Louie. Louie hid , so there were marbles left. Dewey hid 1/3 of the marbles left, so that means there are marbles left. After Daisy took 2 marbles, there are left Huey saw 10 marbles in the pile so, I can say Donald gave Louie 27 marbles check: Louie hid 1/3, or 9 marbles, so there are 18 left Dewey hid 1/3 of these, or so, there are 12 left Daisy took 2, so there are 10 left That's what Huey saw OK
 Travel_Word_Problems/697309: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function . h(t)=100t-16t^2 What is the maximum height that the ball will reach? Height= ? feet Do not round your answer.1 solutions Answer 429862 by josmiceli(9649)   on 2012-12-29 18:33:56 (Show Source): You can put this solution on YOUR website!Plot this function with on the vertical axis and on the horizontal axis. This is a parabola that has a maximum. The maximum is half-way between the 2 roots. One of the roots is at (0,0) at the instant the ball was thrown upward. Find the other root by setting , and find the time when the ball comes back to the ground. The time half-way between and is . Now find the height at The maximum height is 156.25 ft Here's the plot:
 test/697311: how do you find the slop of -5/8x+6=y1 solutions Answer 429856 by josmiceli(9649)   on 2012-12-29 18:13:46 (Show Source): You can put this solution on YOUR website!Write the other way around This is in the form where is the slope and is the y-intercept. So, the slope is