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# Recent problems solved by 'josmiceli'

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 Mixture_Word_Problems/511241: A radiator contains 9 quarts of fluid, 40% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 55% antifreeze?1 solutions Answer 342083 by josmiceli(9697)   on 2011-10-07 17:53:58 (Show Source): You can put this solution on YOUR website!In words: ( final quarts of antifreeze) / ( final quarts of fluid ) = 55% Let = quarts of fluid to be drained and replaced with pure antifreeze given: = quarts of antifreeze in original mixture = quarts of antifreeze that is drained off ------------ 2.25 quarts of fluid should be drained and replaced with pure antifreeze check: OK
 Polynomials-and-rational-expressions/510533: Simplify the eepression: (8x^6y^9)^(2/3)/(16x^8y^-4)^(1/2) I don't know weather to work this like a polynomial and divide. My problem just seems to get longer than shorter. Thank you so much for your help. 1 solutions Answer 341831 by josmiceli(9697)   on 2011-10-06 11:23:38 (Show Source): You can put this solution on YOUR website!You can use the rules for exponents: ------------------- (note that and ) ( and and ) Unless I made a mistake- I would get another opinion, too
 Age_Word_Problems/510514: Zoron is ten years older than his sister. In three years, he will be twice as old as she will be then. How old are they now?1 solutions Answer 341828 by josmiceli(9697)   on 2011-10-06 10:17:06 (Show Source): You can put this solution on YOUR website!Let = Zoron's age now Let = his sister's age now given: ------------------- By substitution: and Zoron is 17 and his sister is 7 check: In 3 years, he will be 20 and she will be 10 OK
 Word_Problems_With_Coins/510170: A parking meter costs .50 for one hour. it takes quarters dimes and nickles how many different combinations are there to equal .50 I came up with an answer of 1901 was I close or way off thank you for your help Alexis 7th grade1 solutions Answer 341741 by josmiceli(9697)   on 2011-10-05 18:46:16 (Show Source): You can put this solution on YOUR website!d - n - q -------- 5 4 - 2 3 - 4 2 - 6 1 - 8 0 - 10 2 - 1 - 1 1 - 3 - 1 0 - 5 - 1 0 - 0 - 2 --------- 10 There are 10 ways to make 50 cents using nickels, dimes, and quarters
 Money_Word_Problems/510063: Mr. Jamison buys a washing machine that is listed at \$800. It is advertised at a 20% discount. At the store, he receives an additional 10% off the sale price, but he discovers that he must pay 6% sales tax on the reduced price of the machine plus a \$40 delivery charge. - I have to write an equation that would represent the final cost of the machine. Thanks!1 solutions Answer 341692 by josmiceli(9697)   on 2011-10-05 16:46:50 (Show Source): You can put this solution on YOUR website!Call the list price Given: I think the equation would be: cost of machine = Just plug in to solve
 Rate-of-work-word-problems/509741: if 10 men take 3 day to complete a piece of work.how may days will 2 men take to complete the same work?1 solutions Answer 341579 by josmiceli(9697)   on 2011-10-04 23:57:38 (Show Source): You can put this solution on YOUR website!10 men take 3 days 1 man will take 10 times as long to finish, or 30 days 2 men will take half of that time, or 15 days
 test/509686: 3 chickens and a duck sold for as much as 2 geese;1chicken, 2 ducks, and 3 geese were sold for \$25.00. What was the price of each bird in exact number of dollars?1 solutions Answer 341578 by josmiceli(9697)   on 2011-10-04 23:48:50 (Show Source): You can put this solution on YOUR website!(1) (2) --------------------- (1) (2) Add the equations: (3) --------------------- There are 3 unknowns and only 2 equations, so it isn't directly solvable, but trial and error might work Suppose g = 6 d = 1 c = 4 Almost (2) (3) Suppose g = 5 d = 4 c = 2 I think this works! (1) (1) (1) (1) OK (2) (2) (2) (2) OK Ducks cost \$4 ea Chickens cost \$2 ea Geese cost \$5 ea
 Expressions-with-variables/509721: I am struggling in the set up of this problem. Can you please help me? The current in a bayou near Lafayette is 4 miles per hour. A paddleboat travels 48 miles up stream in the same amount of time it takes to travel 72 miles downstream. Find the speed of the boat in still water.1 solutions Answer 341574 by josmiceli(9697)   on 2011-10-04 23:13:05 (Show Source): You can put this solution on YOUR website!Let = speed of boat in still water Let = time it takes to go either upstream or downstream is the speed of the current is the boat's speed going downstream is the boat's speed going upstream ------------ given: Going upstream: (1) Going downstream: (2) ------------------- (1) and (2) Subtract (1) from (2) (2) (1) By substitution: (1) (1) (1) (1) The speed in still water is 20 mi/hr check answer: (2) (2) (2) OK
 test/509715: How Could You Change The Pitch of A Roof To Make It Steeper Using Rise And Run?1 solutions Answer 341566 by josmiceli(9697)   on 2011-10-04 23:00:24 (Show Source): You can put this solution on YOUR website!pitch = rise/run The roof gets steeper when rise becomes greater than run, so increasing rise makes it steeper Also decreasing the run makes it steeper
 Age_Word_Problems/509698: rea is 5 years older than jen-jen. in 4 years, rea will be twice as old as jen-jen. how old is each.1 solutions Answer 341565 by josmiceli(9697)   on 2011-10-04 22:57:37 (Show Source): You can put this solution on YOUR website!Let = Rea's age now Let = Jen-Jen's age now given: By substitution: and Jen-Jen is 1 Rea is 6
 Age_Word_Problems/509695: Amy is 7 years older than Tom while Tom is twice as old as Jill. Chris is 3 times as old as Amy. If the sum of Chris and Amy's age is 68. Find Toms age. Please help. i have the answer but my equation is wrong...1 solutions Answer 341559 by josmiceli(9697)   on 2011-10-04 22:46:21 (Show Source): You can put this solution on YOUR website!Let = Amy's age Let = Tom's age Let = Jill's age Let = Chris's age ---------------------- given: (1) (2) (3) (4) -------------- There are 4 unknowns and 4 equations so this should be solvable Substitute (3) into (4) (4) (4) (4) (4) Substitute this result into (1) (1) (1) (1) (1) Substitute this result into (2) (2) (2) (2) and, also (3) (3) (3) ---------------- Amy's age is 17 Tom's age is 10 Jill's age is 5 Chris's age is 51
 Expressions-with-variables/509700: Will you please help me solve for a: 15a-2(4a+5)=-6a 1 solutions Answer 341553 by josmiceli(9697)   on 2011-10-04 22:31:57 (Show Source): You can put this solution on YOUR website! Add to both sides Add to both sides Do the indicated addition and subtraction of terms on the left side -------------- You can check this by putting answer back into original equation I'll use decimal equivilant OK- the error must be due to rounding off
 Angles/509696: one of two complementary angles has a measure that is six more than twice the others. find the measure of the larger angle1 solutions Answer 341547 by josmiceli(9697)   on 2011-10-04 22:19:06 (Show Source): You can put this solution on YOUR website!Call the angles and in degrees given: and The larger angle is 62 degrees
 Mixture_Word_Problems/509429: How much sand must be added to 250 kg of a cement mixture that is 22% sand to have a mixture that is 25% sand?1 solutions Answer 341456 by josmiceli(9697)   on 2011-10-04 18:25:28 (Show Source): You can put this solution on YOUR website!Let = kg of cement to be added given: kg of sand initially ---------- 10 kg of sand must be added check: OK
 Exponents/509418: What does 7.8903^10 to the negative one equals What does 4.4296^10 to the third power equals What does 1^10 to the negative fourth power equals1 solutions Answer 341448 by josmiceli(9697)   on 2011-10-04 18:15:33 (Show Source): You can put this solution on YOUR website!the general rule to follow is: ----------- Use calculator -------------- Use calculator --------------
 Travel_Word_Problems/509378: The Cuyahoga river has current of 2 mph. Two boats start downstream at the same time with one boat 5 miles faster in still water than the other one. How long will it take for the boats to be 25 miles apart if the slower boat can travel 12 miles upstream in 2 hours?1 solutions Answer 341427 by josmiceli(9697)   on 2011-10-04 17:46:33 (Show Source): You can put this solution on YOUR website!Let = time for the boats to be mi/hr is the current mi/hr = speed of slower boat in still water mi/hr = speed of faster boat in still water The slower boat going upstream: mi/hr --------------- Going downstream: slower boat: (1) faster boat: (2) Substitute (1) into (2) (2) (2) (2) In 5 hrs, the boats will be 25 mi apart check answer: (1) (1) mi and (2) (2) (2) OK
 Equations/509189: Please help me solve. Tom, Dave, and Harry went crabbin'. Dave caught 5 more crabs then Tom. Harry caught twice the number Dave caught. They ended the day with 75 crabs. How many crabs did each catch? 1 solutions Answer 341355 by josmiceli(9697)   on 2011-10-04 14:16:07 (Show Source): You can put this solution on YOUR website!Tom, Dave, and Harry caught ,, and number of crabs given: (1) (2) (3) ---------------- (1) Substitute (1) and (2) into (3) (3) (3) (3) and (2) (2) and (1) (1) Tom, Dave, and Harry caught 15, 20, and 40 crabs
 Travel_Word_Problems/509241: A private plan leaves an airport and flies due east at 192 miles per hour. Two hours later, a jet leaves the same airport and flies due east at 960 miles per hour. How far will the private plan fly before it is passed by the jet? 1 solutions Answer 341354 by josmiceli(9697)   on 2011-10-04 14:03:36 (Show Source): You can put this solution on YOUR website!How much of a head start does the private plane get? mi --------------- Now start a stopwatch when the jet leaves For the jet: (1) For the private plane: (2) ( Note that is the same for both, since they are both on the stopwatch now ) --------------- Substitute (1) into (2) hrs The private plane is passed by the jet in 1/2 hr
 Rectangles/509236: The length of a rectangle is five times its width. If the area of the rectangle is 320cm^2 , find its perimeter 1 solutions Answer 341349 by josmiceli(9697)   on 2011-10-04 13:52:32 (Show Source): You can put this solution on YOUR website!The formula for perimeter is: The formula for area is: given: cm2 (1) ---------- (2) (2) Substitute (2) into (1) and, since The length is 40 cm and the width is 8 cm so, the perimeter is cm
 Evaluation_Word_Problems/509208: Find the slope (m) of a line that passes through the following points. (m = - 1/7) (4, 2), (-3, 1) 1 solutions Answer 341331 by josmiceli(9697)   on 2011-10-04 12:44:50 (Show Source): You can put this solution on YOUR website!I get for the slope slope = ( change in y ) / ( change in x )
 Travel_Word_Problems/508978: Flying with a tailwind a jet can fly 2520 miles in 4 hours. Flying against the same wind, it covers 1720 miles in the same amount of time. Determine the speed of the jet in calm air.1 solutions Answer 341216 by josmiceli(9697)   on 2011-10-03 22:28:27 (Show Source): You can put this solution on YOUR website!Let = speed of the jet in calm air Let = speed of wind given: (1) (2) ------------------- (1) (2) Add the equations and, since (2) (2) (2) (2) The speed of the jet in calm air is 530 mi/hr
 test/508955: it is between 50 000 and 52 000. there is a 2 in the tens place. the sum of the digits is 23 1 solutions Answer 341213 by josmiceli(9697)   on 2011-10-03 22:13:55 (Show Source): You can put this solution on YOUR website!The ten-thousands digit is The thousands digit is either or The tens digit is So far, I have either 50a2b or 51a2b In the 1st case, In the 2nd case, What's the question? There are lots of possible answers
 Permutations/508959: How many different 4-letter radio call letters can be made using the 26 capital letters of the English alphabet (Examples: WJBR, KDKA, WSTW) if the first letter must be K or W and no letter may be repeated.1 solutions Answer 341191 by josmiceli(9697)   on 2011-10-03 21:32:16 (Show Source): You can put this solution on YOUR website!There are possible choices for the 1st letter Repetitions are not allowed, so there are choices for the 2nd letter for the 3rd letter for the 4th letter Multiply possible choices to get all possible combinations of letters There are 27600 possible 4-letter radio call signs
 Mixture_Word_Problems/508940: I have a 70% meat and30% meat need to get 37% but it has to weigh 3060pounds1 solutions Answer 341182 by josmiceli(9697)   on 2011-10-03 21:24:25 (Show Source): You can put this solution on YOUR website!Let = pounds of 70% meat needed Let = pounds of 30% meat needed given: (1) pounds (2) -------------------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) 535.5 pounds of 70% meat are needed 2524.5 pounds of 30% meat are needed check answer: (2) (2) (2) (2) (2) OK
 Word_Problems_With_Coins/508726: paul has twice as many dimes as pennies and 3 times as many nickels as pennies. in all he has 1.80? how many coins of each type does he have?1 solutions Answer 341091 by josmiceli(9697)   on 2011-10-03 18:31:11 (Show Source): You can put this solution on YOUR website!Let = number of pennies Let = number of nickels Let = number of dimes given: (1) (2) (3) ( in pennies ) Substitute (1) and (2) into (3) (3) (3) (3) (3) and (1) (1) and (2) (2) There are 5 pennies, 15 nickels, and 10 dimes check answer: (3) (3) (3) (3)
 Complex_Numbers/508737: What is the answer to 6 over 9+i?1 solutions Answer 341082 by josmiceli(9697)   on 2011-10-03 18:08:20 (Show Source): You can put this solution on YOUR website! answer
 Travel_Word_Problems/508036: One morning Madeline drove 5 hours before stopping to eat. After lunch, she increased her speed by 10mph in order to complete a 430-mile trip in 8 hours of driving time. How fast did Madeline drive in the morning?1 solutions Answer 340845 by josmiceli(9697)   on 2011-10-02 17:11:56 (Show Source): You can put this solution on YOUR website!Let = her speed before lunch = her speed after lunch hrs driving time after lunch Let = distance she drove before lunch = distance she drove after lunch ------------- Before lunch: (1) After lunch: (2) Substitute (1) into (2) (2) (2) (2) (2) She drove 50 mi/hr in the morning check: (1) (1) and (2) (2) OK
 Problems-with-consecutive-odd-even-integers/508028: is this always, sometimes or never true? the sum of 3 consecutive odd integers equals an even integer.1 solutions Answer 340843 by josmiceli(9697)   on 2011-10-02 17:00:24 (Show Source): You can put this solution on YOUR website!It is never true An odd number is always: even + 1 So 2 odd numbers are: even + 1 + even + 1 = 2 x even + 2 which is obviously even Now to an even number you add an odd, which is even + 1 Now you have even + even + 1 = even + 1 which is always odd
 Money_Word_Problems/508033: johnston and betsy have a jar containing 80 coins of which are either quarters or nickels. the total value of the coins is \$14.60 how many of each coin do they have? i need the equations please!1 solutions Answer 340840 by josmiceli(9697)   on 2011-10-02 16:53:52 (Show Source): You can put this solution on YOUR website!Let = number of nickels Let = number of quarters given: (1) (2) ( in cents ) --------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) They have 27 nickels and 53 quarters check answer: (2) (2) (2) OK
 Numbers_Word_Problems/507904: how do i solve this problem,- The hundreds digit of a three-digit number is 2 more than the units digit. The digits of the original three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result? Describe anything interesting you discover finding the solution. You need to try this out on at least three 3-digit numbers of your choosing.1 solutions Answer 340796 by josmiceli(9697)   on 2011-10-02 13:45:12 (Show Source): You can put this solution on YOUR website!Call the digits a,b, and c The number is abc given: a = c + 2 abc - cba The units digit will be c - (c + 2) , but to do this, you have to carry 10 over to the c, and you have 10 + c - (c + 2) = 8 check: abc = 553 cba = 355 553 - 355 = 198 --------------- abc = 917 cba = 719 917 - 719 = 198 --------------- abc = 391 cba = 193 391 - 193 = 198 --------------- The result is always 198
 Numbers_Word_Problems/507886: what is the sum of the first 30 odd numbers? 1 solutions Answer 340790 by josmiceli(9697)   on 2011-10-02 13:23:50 (Show Source): You can put this solution on YOUR website! (2 numbers) (3 numbers) ( 4 numbers) So, the sum of the 1st 30 odd integers is