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# Recent problems solved by 'josmiceli'

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 Mixture_Word_Problems/651004: A certain metal is 40% copper. How many kilograms of this metal must be mixed with 60 kilograms of a metal that is 70% copper to get a metal that is 50% copper?1 solutions Answer 407525 by josmiceli(9697)   on 2012-09-13 17:45:58 (Show Source): You can put this solution on YOUR website!Let = kg of 40% metal needed = kg of copper in 40% metal kg of copper in 70% metal 120 kg of the 40% metal are needed check: OK
 Age_Word_Problems/651003: Micheal is 4 as old as Jackie. In 4 years, he will be twice as old as she will be then. How old is each now? Can you please give and example if how to show the work because I am lost1 solutions Answer 407523 by josmiceli(9697)   on 2012-09-13 17:35:26 (Show Source): You can put this solution on YOUR website!Is the 1st sentence "Michael is 4 TIMES as old as Jackie." ? If so, Let = Michael's age now Let = Jackie's age now = Michael's age in 4 years = Jackie's age in 4 years ------------------------- given: (1) (2) ----------------------- These are 2 equations with 2 unknowns so it's solvable (2) Substitute (1) into (2) (2) (2) (2) and, since (1) (1) (1) -------------- Michael is 8 and Jackie is 2 check: (2) (2) (2) (2) OK (1) (1) (1) OK
 Travel_Word_Problems/650348: two people walk daily for exercise. One is able to maintain 4.0mph and the other only 3.5mph. The slow walker has a mile head start when the other begins, yet they finish together. How far did each walk?1 solutions Answer 407298 by josmiceli(9697)   on 2012-09-12 17:49:33 (Show Source): You can put this solution on YOUR website!The slow walker has a head start of 1 mile Let = the distance in miles that the fast walker covers -------------- Now time both of them after the head start Let = the time for both slow walker: (1) Fast walker: (2) ------------- Substitute (2) into (1) (1) (1) (1) ------------ and, since (2) (2) (2) Each walked the entire distance of 8 miles check: Slow walker's time during head start was So his time for the whole 8 miles was hrs OK
 Probability-and-statistics/650346: 16 out of 100 students eat ice cream at lunch. what decimal represents the number of students that eat ice cream? 1 solutions Answer 407290 by josmiceli(9697)   on 2012-09-12 17:20:48 (Show Source):
 Numbers_Word_Problems/650340: What are two odd consecutive numbers that have a product of 12,099 1 solutions Answer 407289 by josmiceli(9697)   on 2012-09-12 17:18:53 (Show Source): You can put this solution on YOUR website!Let the numbers be and given: complete the square The number are 109 and 111 check: OK
 Polynomials-and-rational-expressions/650332: 2x^2-3x-20 / 4x^2-13x-12 = I tried to factor the bottom and the top and then kinda got stuck the directions say to reduce to lowest terms. I come up with (x-4)(2x+5) on top and (x-4)(4x+3) I am just unsure where to go from here Can you help please? 1 solutions Answer 407286 by josmiceli(9697)   on 2012-09-12 17:10:29 (Show Source): You can put this solution on YOUR website! It helps to express it like this: You can see that the 1st fraction is , so reduced to lowest terms this is
 Travel_Word_Problems/650320: Mike drove to a friends house at a rate of 40 miles mph. The return trip he traveled at a rate of 45 mph. Total driving time was 4 hours. What is the distance Mike traveled?1 solutions Answer 407281 by josmiceli(9697)   on 2012-09-12 16:57:55 (Show Source): You can put this solution on YOUR website!Let = distance to friend's house in miles Let = time in hrs to drive to friend's house given: To friend's house: (1) Return trip: (2) ------------------- Substitute (1) into (20 (2) (2) (2) (2) (2) Plug this result back into (1) or (2) (1) (1) (1) and Mike traveled 169.412 mi check: (2) (2) (2) (2) (2) OK
 Bodies-in-space/650148: I need help with a Precalculus problem: The weight, W, of an object varies inversely as the square of the distance, d, from the center of the earth. At sea level (3978 mi from the center of the earth), an astronaut weighs 220 lb. Find their weight when they are orbiting 400 mi above sea level. 1 solutions Answer 407256 by josmiceli(9697)   on 2012-09-12 15:16:44 (Show Source): You can put this solution on YOUR website! is called the constant of proportionality given: pounds mi --------------- The astronaut weighs about 200 pounds
 Square-cubic-other-roots/650133: My buddy buddy needs help: ([2^2]^3 g^4 h^4)^31 solutions Answer 407197 by josmiceli(9697)   on 2012-09-12 11:08:10 (Show Source): You can put this solution on YOUR website! Whenever you have parentheses, work from the inside out. So start with ---------------------- The general rule for this is: , so ---------------------- -------------------- Now you have: Note that answer --------------------------- You can check this by filling in any numbers for and ------------- Plug in same numbers for answer: This should be the same as This doesn't PROVE the answer's right but there is a better than even chance
 Travel_Word_Problems/650135: It took an airplane hours to fly mi against a headwind. The return trip with the wind took hours. Find the speed of the plane with no wind and the windspeed. The speed of the plane is ____ mph. The windspeed is _____ mph. 1 solutions Answer 407187 by josmiceli(9697)   on 2012-09-12 10:23:07 (Show Source): You can put this solution on YOUR website!Please fill in data
 Travel_Word_Problems/650123: a car goes down a street at 26 miles an hour two hours later another one goes down the same street at how long will it take for the second car to catch up to the first when its going 52 miles an hour1 solutions Answer 407186 by josmiceli(9697)   on 2012-09-12 10:21:34 (Show Source): You can put this solution on YOUR website!The 1st car has a head start of mi Start a stopwatch when you see the 2nd car Stop the stopwatch when the 2nd car catches the 1st Call that time Let = the distance that the 2nd car travels ----------------- Equation for 1st car: (1) Equation for 2nd car: (2) -------------- Substitute (2) into (1) (1) (1) (1) hrs The 2nd car catches the 1st car in 2 hrs check answer: (1) (1) (1) (1) mi and (2) (2) (2) mi OK
 Linear-equations/650131: Find an equation of a line that has an x intercept of 6 and a y intercept of 41 solutions Answer 407181 by josmiceli(9697)   on 2012-09-12 10:03:03 (Show Source): You can put this solution on YOUR website!This means the line goes through (6,0) and (0,4) The slope is ( change in y ) / ( change in x ) ---------- The general form is = slope = y-intercept ------------------ answer Here's the plot:
 Exponents/650129: 7.6+10^-2 times .0076x10^-3 divided by 1.2x10^-10. Thank you for your time.1 solutions Answer 407179 by josmiceli(9697)   on 2012-09-12 09:56:28 (Show Source): You can put this solution on YOUR website! You only need 2 rules: and And, what amounts to the same thing, --------------------- Simplify a little Hope I got it
 Coordinate-system/649651: What if i'm to scared to ask for help because i think i will get laughed at but i still don't understand it; what do i do then? 1 solutions Answer 407039 by josmiceli(9697)   on 2012-09-11 16:28:49 (Show Source): You can put this solution on YOUR website!I've been there. But if you don't say " I'm lost" when you're lost, you'll just stay lost. ---------- Minimize embarrassment if you can, but math is something where the basics have to be very clear or you can't move on. Good luck
 Word_Problems_With_Coins/649635: Abby has 36 coins, consisting only of dimes and quarters, worth \$7.95. How many dimes and how many quarters does she have?1 solutions Answer 407029 by josmiceli(9697)   on 2012-09-11 16:23:15 (Show Source): You can put this solution on YOUR website!There must be an odd number of quarters, since the sum ends in a 5. If there was an even number, it would end in 0. ------------------ I will try 29 quarters. That comes to or \$.70. That is 7 dimes coins ------------------- There are 29 quarters and 7 dimes
 Age_Word_Problems/649495: Joseph age 5 years from now is 17 what is the algebraic equation of this1 solutions Answer 406974 by josmiceli(9697)   on 2012-09-11 11:30:07 (Show Source): You can put this solution on YOUR website!Let = his age now
 Travel_Word_Problems/649492: A man cycles from his office to his house at a speed of 5 km/hr and reaches 10 minutes late. If he cycles at a speed of 6 km/hr, he reaches 10 minutes early. What is the distance between the office and his house? 1 solutions Answer 406972 by josmiceli(9697)   on 2012-09-11 11:24:52 (Show Source): You can put this solution on YOUR website!Let = the distance in km between house and office Let = The travel time in hrs which is on time for him given: From office to house at 5 km/hr (1) From office to house at 6 km/hr (2) ----------------------- (1) (2) ---------------- Substitute (1) into (2) (2) (2) (2) Plug this result back into (1) or (2) (1) (1) (1) the distance between his house and office is 10 km check: (2) (2) (2) (2) OK (1) (1) (1) (1) (1) (1) OK
 Age_Word_Problems/649341: Jenifer is 20 years old and her sister is 4 years old. In how many years will Jenifer be four times as old as her sister?1 solutions Answer 406929 by josmiceli(9697)   on 2012-09-11 01:36:12 (Show Source): You can put this solution on YOUR website!Add years to both their ages given: ( note that 1/3 year = 4 months ) In 1 year and 4 months Jennifer will be 2x as old as her sister check: J will be Sis will be OK
 Rate-of-work-word-problems/649267: Next door neighbors Bob and Jim use hoses from both houses to fill Bobs swimming pool. They know that it takes 18 hours to fill using both hoses. They also know that Bobs hose, used alone, takes 20% less time than Jims hose alone. How much time would is required to fill the pool by each hose alone? .. I am having a hard time showing my work, not neccesarily getting the answer but id aprreciate any help1 solutions Answer 406903 by josmiceli(9697)   on 2012-09-10 21:58:46 (Show Source): You can put this solution on YOUR website!Let = time in hrs for Jim's hose alone to fill pool = time in hrs for Bob's hose alone to fill pool ------ Add their rates of filling to get rate filling together Multiply both sides by 40.5 = time in hrs for Jim's hose alone to fill pool 32.4 = time in hrs for Bob's hose alone to fill pool check: OK
 Travel_Word_Problems/648831: Train Speed: A train leaves Los Angeles at 2:00 PM. A second train leaves the same station in the same direction at 4:00 PM. The second train travels 24 mph faster than the first. If the second train overtakes the first at 7:00 PM, what is the speed of each of the two trains? I am not sure how to construct an equation to solve this problem. Thanks for your help!1 solutions Answer 406842 by josmiceli(9697)   on 2012-09-10 15:54:50 (Show Source): You can put this solution on YOUR website!Let the speed of the 1st train = = the speed of the 2nd train Let = the head start that the 1st train got 4 PM - 2PM is hrs, so Let = the distance that the 2nd train has to go to catch the 1st train ---------------- 7PM - 4PM = hrs Use this time for both trains. Figure that the 1st train already has the head start ----------------- 1st train's equation: (1) ----------------- 2nd train's equation: (2) ---------------------- (1) and (2) ------------------ Substitute (1) into (2) (2) (2) (2) also --------------- The 1st train's speed is 36 mi/hr The 2nd train's speed is 60 mi/hr check: So, the 1st train had a head start of 72 mi which took 2 hrs. Now it has 3 hrs to go the rest of the way 2nd train's equation: (2) (2) (2) mi mi The 1st train must go 108 mi in 3 hrs at 36 mi/hr OK
 Miscellaneous_Word_Problems/648871: there are 40 rooms that need to be painted and only 6 painters available, if there are still 10 rooms unpainted, how many rooms did each painter paint1 solutions Answer 406828 by josmiceli(9697)   on 2012-09-10 15:24:54 (Show Source): You can put this solution on YOUR website!The 6 painters must have painted rooms Each painter painted 5 rooms ( That's if they all paint at the same rate , which is assumed )
 Word_Problems_With_Coins/648794: liviana has \$ 2.20 in coins in her change purse. if there is a total of 15 coins how many quarters,dimes,nickles,and pennies does she have?1 solutions Answer 406825 by josmiceli(9697)   on 2012-09-10 15:20:05 (Show Source): You can put this solution on YOUR website!There are 4 unknowns but only 2 possible equations, so this can't be solved directly, but it still can be figured out. Let = number of pennies Let = number of nickels Let = number of dimes Let = number of quarters The equations are: (1) (2) ( in cents ) ------------------------------------------ The logic steps are: (a) There doesn't have to be any pennies, although there might be, but they will be in multiples of 5 or 10 (b) I know there must be less than 9 quarters, since 9 x 25 = 225, which is too much (c) I know there must be more than 2 quarters since 2 x 25 = 50, that leaves 13 coins to make \$1.70 and even if I have 13 dimes, that is only \$1.30 (d) Likewise, there must be more that 3 quarters 3 x 25 = 75 and 220 - 75 = 145, and 12 x10 = 120 which doesn't make it (e) Also, there must be more than 4 quarters 4 x 25 = 100 and 220 - 100 = 120 There are 11 coins left to make \$1.20 and 11 x 10 = 110, too small (f) It is possible with 5 quarters since 5 x 25 = 125 and 220 - 125 = 95 and 10 x 10 = 100, so it's possible -------------------------------- 5q = 125 which is 5 coins leaving 10 220 - 125 = 95 9d = 90 leaving 1 coin 1 x 5 = 5 So, the answer is 5q 9d 1n But if I have to use pennies it doesn't work -------------------------- I'll try 6q 5d 4n This works, but still no pennies --------------------------- I'll try 7q 1d This leaves 7 coins to make 35 cents and no room for pennies --------------------- 8q 1d Leaves 6 coins to make 10 cents that's 1n 5p That's it ------------ 8 quarters, 1 dime, 1 nickel, and 5 pennies are 15 coins that make \$2.20
 Travel_Word_Problems/648758: A jet plane traveling at 550 mph overtakes a propeller plane traveling at 200 mph with a two hour head start. How far from the starting point are the planes?1 solutions Answer 406795 by josmiceli(9697)   on 2012-09-10 12:16:10 (Show Source): You can put this solution on YOUR website!First find the head start of the prop plane in miles mi Start a stopwatch when the jet leaves Now they will both fly for the same amount of time until jet catches prop Let = distance jet travels Let = time on stopwatch -------------------------------- Jet's equation: (1) prop's equation: (2) --------------------- Substitute (1) into (2) (2) (2) (2) hrs --------------- (1) (1) The planes are 628.57 mi from the start ( unless I miscalculated )
 Percentage-and-ratio-word-problems/648761: 35% of a class are female 60% of the females have blue eyes 38% of males have blue eyes what % of the class have blue eyes have done 60% of 35 = 21 38% of 65 = 24.7 21+24.7 = 45.7 believe answer is 45.7% 1 solutions Answer 406791 by josmiceli(9697)   on 2012-09-10 11:54:57 (Show Source): You can put this solution on YOUR website!60% of 35% of the class are the females with blue eyes 21% of the class are females with blue eyes --------------- If 35% of the class are females, 65% are males and 38% of 65% have blue eyes 24.7% of the class are males with blue eyes --------------- 45.7% of the class has blue eyes
 Linear_Equations_And_Systems_Word_Problems/648711: a group of boys and girls are playing.when 15 boys leave,their remains 2 girls for each boy. then when 45 girls leave their remains 5 boys for each girl.how many boys were there in original group?1 solutions Answer 406777 by josmiceli(9697)   on 2012-09-10 10:26:35 (Show Source): You can put this solution on YOUR website!Let = number of boys in original group Let = number of girls in original group -------------- When 15 boys leave, you have boys and girls, and you are given that (1) ------------------- When 45 girls leave, you have boys girls You are given that (2) -------------------------- (1) (1) and (2) (2) -------------------- Multiply both sides of (1) by and add the equations (1) (2) There were 40 boys in the original group check: (1) (1) (1) (1) and (2) (2) (2) (2) (2) OK
 Linear-equations/648740: find the slope of (0,1)and(3,0)1 solutions Answer 406775 by josmiceli(9697)   on 2012-09-10 10:10:25 (Show Source): You can put this solution on YOUR website!Slope = ( change in y ) / ( change in x ) slope = ( 0 - 1 ) / ( 3 - 0 ) slope = -1 / 3
 Linear-systems/648721: flying with the wind, a bird has a speed of 90kph.but flying against the wind of only half that speed, it only made 30kph. find the speed of the wind and the bird's rate of flying when there is no wind.1 solutions Answer 406773 by josmiceli(9697)   on 2012-09-10 10:07:23 (Show Source): You can put this solution on YOUR website!Let = bird's speed with no wind Let = the speed of the wind = half of the wind speed = bird's speed flying against the wind = bird's speed flying with the wind ------------ given: (1) (2) ------------------- Multiply both sides of (2) by (2) (2) and (1) ----------------- add the equations and, since (1) (1) (1) The bird's speed with no wind is 50 km/hr The speed of the wind is 40 km/hr check: (2) (2) (2) (2) and (1) (1) (1) OK
 expressions/648739: Please help me solve this equation : A loss of 1/3 of an investment of d dollars.1 solutions Answer 406771 by josmiceli(9697)   on 2012-09-10 09:54:06 (Show Source): You can put this solution on YOUR website!You can write that as I words, this is: ( what you started with ) - ( what you lost ) = what you have left
 Numbers_Word_Problems/648723: Some children are sharing oranges among themselves.If each gets 9 orange, no orange will be left. If each gets 6, then 18 will be left over. How many children are there?1 solutions Answer 406770 by josmiceli(9697)   on 2012-09-10 09:50:07 (Show Source): You can put this solution on YOUR website!It isn't stated exactly, but there must be a fixed number of oranges that are being shared. Let = the number of children With each one getting 9 oranges, there are oranges in all. and If each child gets 6 oranges, there are oranges in all. ------------------------- In both cases, the number of oranges hasn't changed, so There are 6 children ------------------ check: If each gets 9 oranges, that is ------------------ If each gets 6 with 18 left over, that is OK
 Geometry_Word_Problems/648731: a college offers nine different psychology courses, four different history courses , thirteen different math courses , and five different business courses. If a student is required to take one course in each of these four subjects , how many different ways are there for the student to fulfill this requirement? Show your work1 solutions Answer 406766 by josmiceli(9697)   on 2012-09-10 09:34:41 (Show Source): You can put this solution on YOUR website!There are 4 history courses any 1 of which can be taken with any 1 of 9 psych courses. That is Any 1 of these 36 choices can be taken with any 1 of 13 math courses. That is so far Any 1 of these 468 choices can be taken with any 1 of 5 business courses. That is answer or, you could write it in 1 line: