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# Recent problems solved by 'josmiceli'

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 Money_Word_Problems/221223: how many tons of hay at \$125 per ton and \$75 per ton must be purchased to have 100 tons of hay worth \$9000?1 solutions Answer 165990 by josmiceli(9661)   on 2009-10-04 01:21:56 (Show Source): You can put this solution on YOUR website!Let = tons of \$125/ton hay used Let = tons of \$75/ton hay used given: (1) (2) --------------------------- Multiply both sides of (1) by and subtract from (2) (2) (1) and, since 30 tons of \$125/ton hay and 70 tons of \$75/ton hay must be purchased check: (2) OK
 Linear-equations/221111: x=number of white paint can y=number of blue paints can x=y=5 cans of paint white paint = \$ 24 blue paint = \$ 28 24x + 28y = \$132 How do you solve: 24x + 28y = 132 ? How steps.1 solutions Answer 165891 by josmiceli(9661)   on 2009-10-03 17:24:19 (Show Source): You can put this solution on YOUR website!You can't solve it. There are 2 variables, x and y, so you need 2 equations to solve. You wrote . I think you mistyped & actually meant That's your other equation Multiply both sides of this equation by Now subtract it from the other equation and, since Hope this helps
 Permutations/220982: A single die is rolled twice. Find the probability of rolling an odd number the first time and a number less than 3 the second time. thank you for your help!1 solutions Answer 165777 by josmiceli(9661)   on 2009-10-03 11:44:02 (Show Source): You can put this solution on YOUR website!The 6 sides of the die are numbered 1,2,3,4,5,6 There are 3 odd and 3 even numbers probability of an odd number on 1st roll is When you want A AND B probabilities, you multiply the events A and B The number less than 3 are 1,2, so the probability is And the probability of getting both these events is
 Quadratic_Equations/220887: I don't understand how to use the formula of ax^+bx+c=0 My problem is this x^2+7x=180 I need x answered1 solutions Answer 165739 by josmiceli(9661)   on 2009-10-03 01:07:38 (Show Source): You can put this solution on YOUR website!The equation is called quadratic, or 2nd degree. When you plot it on a graph, it's called a parabola. It's in the form , but first subtract from both sides, and it will be in that form Matching it up with the general equation, Now use the quadratic formula to solve 769 isn't a perfect square- are you sure you copied this right?
 Miscellaneous_Word_Problems/220907: When the Johnson triplets were three weeks old, their sleep habits were remarkably consistent. John slept for 3 hours and was awake for 30 minutes. Joan slept for 2 hours and was awake for 30 minutes. Jane slept for 2 hours 20 minutes and was awake for 40 minutes. On October 13 at 8:00 P.M., they all went to sleep at the same time. When did this event occur again? Give both the date and time. 1 solutions Answer 165737 by josmiceli(9661)   on 2009-10-03 00:55:49 (Show Source): You can put this solution on YOUR website!Each one has a different sleep-awake cycle: John's is hrs Joan's is hrs Jane's is hrs Call the lengths of these cycles ,, and Now I can say Note that , and Finally, I can say 60 sleep-awake cycles for John, 84 sleep-awake cycles for Joan and 70 sleep-awake cycles for Jane all end together 210 hours from Oct 13, 8 PM days and hours 8 days would make it Oct 21, 8 PM Adding 18 hours makes it Oct 22, 2 PM they all go to sleep again at the same time check answer For John: OK
 Exponential-and-logarithmic-functions/220853: Dear Tutor, Please help me solve this tedious math problem. Your help is GREATLY appreciated. Thanks so much!!! :) By the way, I need to solve by factoring the square 4x^2-4x-99=01 solutions Answer 165726 by josmiceli(9661)   on 2009-10-03 00:19:22 (Show Source): You can put this solution on YOUR website! First divide both sides by Now add to both sides Now take 1/2 of the coefficient of which is , square it, and add it to both sides Notice that both sides are perfect squares I'll take the square root of both sides There is also a negative square root The roots are and I'll plot it to verify Looks about right
 Exponents-negative-and-fractional/220863: i don't get negative numbers please explain1 solutions Answer 165689 by josmiceli(9661)   on 2009-10-02 19:46:10 (Show Source): You can put this solution on YOUR website!Sometime a negative number seems like a ghost and sometimes it's clearly visible. It depends on what you're using them for. (A) Let's say I'm on a railroad track that runs east and west. If I want to, I can say that if I go west, that's positive motion, and if I go east, that's negative motion. OK, I go W 1 mile, I go E 2 miles, then I go W 6 miles. How far am I from where I started? I went W +1 miles I went E -2 miles I went W +6 miles 1 - 2 + 6 = +5 miles I am 5 miles west of where I started. (B) Let's say I owe you \$5. I've got the \$5, so it's a (+) on my records until it's spent. You're missing the \$5, so it's a (-) on your records until I pay it back. What does -\$5 look like? Nobody's ever seen one, but recordkeeping can't work without it. Think of it as an empty pocket that only holds a single \$5 bill, and you're always reminded that it's empty and needs to be filled. It's the -\$5 pocket. Does that help at all? You need to keep thinking about it.
 Systems-of-equations/220821: this is a word problem i cant figure it out please help: one canned juice drink is 20% orange juice, another os 10% orange juice. How many liters pf each should be mixed togethre in order to get 10L that is 12% orange juice?1 solutions Answer 165686 by josmiceli(9661)   on 2009-10-02 19:24:06 (Show Source): You can put this solution on YOUR website!Let = liters of 20% juice needed Let = liters of 10% juice needed given: (1) liters of 12% mixture OJ in 20% juice is liters OJ in 10% juice is liters OJ in 12% juice is liters In words: (liters OJ in 20% mix + liters OJ in 10% mix)/(total liters of 12% mix) = 12% (2) Subtract (1) from (2) (2) (1) liters and, since liters 2 liters of the 20% juice and 8 liters of the 10% juice need to be mixed check answer: OK
 Miscellaneous_Word_Problems/220828: I'm taking algebra but I have a hard time with word problems. Please help. 1) A certain granola mixture is 10% peanuts. A) If a container has 20 lbs. of granola how many pounds of peanuts does it contain? B) If a container has X lbs. of granola in it write an expression for the amount of peanuts it contains. Thank you for any help! 1 solutions Answer 165681 by josmiceli(9661)   on 2009-10-02 17:59:41 (Show Source): You can put this solution on YOUR website!(A) 10% of 20 pounds is: It contains 2 pounds of peanuts (B) 10% of pounds is: pounds of peanuts
 Quadratic_Equations/220641: Sammy spends 10 Euros on some cans of drink. In another shop she sees that the same cans are each 10 cents cheaper, and she calculates that she could have brought 5 more cans for the same money. How many cans did she buy?1 solutions Answer 165604 by josmiceli(9661)   on 2009-10-02 10:09:36 (Show Source): You can put this solution on YOUR website!Let = number of cans bought given: = price per can in euros In the other shop, price per can = The same money is euros, so by quadratic equation: (reject the negative solution) She bought 20 cans check answer: OK
 Linear-equations/220660: I have word problem. A medium pizza costs \$10.95, a large pizza costs \$14.95. On a given day 50 pizzas were sold at a cost of \$663.50. How many medium and how many large pizzas were sold. How do I set this up thanks.1 solutions Answer 165597 by josmiceli(9661)   on 2009-10-02 09:36:12 (Show Source): You can put this solution on YOUR website!Let = number of medium pizzas sold Let = number of large pizzas sold given: (1) = cash received for pizzas (in cents) ------------------ = cash from medium pizzas (in cents) = cash from large pizzas (in cents) (2) I have 2 equations with 2 unknowns, so it's solvable Multiply both sides of (1) by and subtract from (2) (2) (1) and, since (1) 21 medium and 29 large pizzas were sold check answer: (2) OK
 Travel_Word_Problems/220538: Rick robbed a bank and left town at 64 mph. His crime was discovered 45 minutes later when the sheriff took off in hot pursuit at 80 mph. How long until the sheriff catches up?1 solutions Answer 165544 by josmiceli(9661)   on 2009-10-01 22:39:33 (Show Source): You can put this solution on YOUR website!Assume I have a stopwatch. I will start the stopwatch when the sheriff leaves. At that time, Rick has travelled (45 min is 3/4 of an hour) mi So, Rick has a 48 mi headstart From this headstart to where the sheriff catches him, call in miles For the sheriff: For Rick: By substitution: hrs The sheriff catches him 3 hrs after the sheriff leaves town check answer: (for Rick) mi So, Rick went a total of mi at mi/hr The sheriff went mi also at mi/hr For Rick: hrs for the whole trip for Rick For Sheriff: hrs for the whole trip for Sheriff Note that , which is the 45 min headstart that Rick had
 Money_Word_Problems/220551: At the Glamour Boutique, a bottle of Allura Numero 75 perfume costs as much as two bottles of Exotic Mist. Mrs. Hampton bought one bottle of each and paid \$24.00. How much does a bottle of Allura cost?1 solutions Answer 165535 by josmiceli(9661)   on 2009-10-01 22:15:58 (Show Source): You can put this solution on YOUR website!Let = cost per bottle of Allura Let = cost per bottle of Exotic Mist given: By substitution: and A bottle of Allura cost \$16
 Travel_Word_Problems/220543: I need help solving the problem: The Great Seto Bridge in Japan is about 7.6 mi long. How long would it take you to cross the bridge if you were walking at 3mi/hr? This is what I have done: I set up a chart: Rate:4 Time:t Distance:7.6 So would it be 4t=7.6? I have no idea what I am doing. Please help. Your guidance would be greatly appreciated. Thank you. -Michelle (Freshman)1 solutions Answer 165531 by josmiceli(9661)   on 2009-10-01 22:09:42 (Show Source): You can put this solution on YOUR website! given: mi/hr mi Divide both sides by hrs It would take 1.9 hrs to cross bridge
 Mixture_Word_Problems/220473: Help with word problem for Algebra 1 The nutty food company sells trail mixes by the pound. There are peanuts, raisin, ans carob-coated pretzels. The mgr. wants to make 80 pounds of this mixture and sell it for \$3.35 per pound. Peanuts sell for \$ \$3.20 per pound, raisins sell for \$ 2.40 per pound, and the carob pretzels sell for for \$4.00 per pound. If the mixture has TWICE as many pounds of pretzels as raisons, how many pounds of each ingredient should the clerk use?1 solutions Answer 165527 by josmiceli(9661)   on 2009-10-01 22:03:54 (Show Source): You can put this solution on YOUR website!Let = pounds of peanuts needed Let = pounds of raisins needed Let = pounds of carob pretzels needed given: (1) (2) (2) Cost of peanuts in mixture = Cost of raisins in mixture = Cost of Carob pretzels in mixture = -------------------------------------------- (3) (3) (units are cents) Multiply both sides of (1) by and subtract from (3) (3) (1) Divide both sides by Substitute this result and (2) in (1) (1) and and The clerk should use 35 lbs of peanuts, 15 lbs of raisins, and 30 lbs of carob-coated pretzels check answer: OK
 real-numbers/220463: Find a number between 11/12 and 1.1 solutions Answer 165500 by josmiceli(9661)   on 2009-10-01 20:32:35 (Show Source): You can put this solution on YOUR website!If I add to I get , so I need a fraction less than . One-half of is 23/24 is a number between 11/12 and 1 check: OK
 Money_Word_Problems/220203: A bookstore priced all hardback books at \$5 a book and all paper back books at \$1. The store sold 30 more paper backs than hardbacks. Total sales were \$354. How many of each type were sold. 1 solutions Answer 165394 by josmiceli(9661)   on 2009-10-01 13:55:39 (Show Source): You can put this solution on YOUR website!Let = number of hardbacks soold Let = number of paperbacks sold given: (1) and (2) Multiply both sides of (1) by and add to (2) and 84 paperbacks and 54 hardcovers were sold check answer: (2) OK
 Money_Word_Problems/220231: I know the answer is 2014. I just don't understand how this was calculated. Please help me. Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at \$44,000 with a raise each March 1 of 2%. Chris starts at \$28,000 with a raise on March 1 each year of 6%. In what year will Chris' salary exceed Sonja's?1 solutions Answer 165391 by josmiceli(9661)   on 2009-10-01 13:45:29 (Show Source): You can put this solution on YOUR website!The situation can be modelled as 2 linear equations Let Salary, , be plotted on the vertical axis Let Years, , be plotted on the horizontal axis (staring at zero) For Sonja, (1) For Chris, (2) I can rewrite them as (1) (2) I'll find out in what year Salaries are equal Divide both sides by 28000 Their salaries will be equal in 20 years Chris's will exceed Sonja's in 21 years, or March 1st, 2022. If you're sure the answer is 2014, then I made a mistake, but I think the method is OK. I'll plot them:
 Triangles/220233: Find the altitude of an equilateral triangle that has side lengths of 4y. Express your answer in simplest radical form. I am a homeschooling mom and don't remeber how to do this. Our book doesnt help either.1 solutions Answer 165378 by josmiceli(9661)   on 2009-10-01 13:11:33 (Show Source): You can put this solution on YOUR website!The interior angles of an equilateral triangle are 60-60-60, which adds up to 180 degrees, as they should. The altitude divides the triangle into two 30-60-90 triangles, with the altitude being opposite the 60 degree angle. Call the altitude In this right triangle, , and Solve for
 Probability-and-statistics/220227: Two cards are drawn in succession from an ordinary deck of 52 bridge cards without replacement of the first card. Find the probability that both cards are a Queen. 1 solutions Answer 165376 by josmiceli(9661)   on 2009-10-01 12:58:18 (Show Source): You can put this solution on YOUR website!There are 4 queens, so on the 1st draw the probability of getting one is Now there are cards in the deck, and if you got a queen, there are 3 queens left The probability of getting one is When you want the probability of getting A and B you multiply, so The probability of drawing 2 queens in a row is 1/221
 Mixture_Word_Problems/220223: I can't figure this one out and it's due yesterday! please help! i can do the conversion part, but factoring in the '18%' is stumping me... thank you! {{You work in a factory that makes chocolate chip cookies. Your cookies contain 18% by weight chocolate chips. If your boss tells you that yesterday, the factory used up 300 lbs. of chocolate chips, how many kilograms of cookies did the factory make?}}1 solutions Answer 165375 by josmiceli(9661)   on 2009-10-01 12:49:54 (Show Source): You can put this solution on YOUR website!Let = pounds of cookies the factory made lbs lb = kg lbs x kg/lb = kg The factory made 755.983 kg of cookies
 Travel_Word_Problems/219900: One lawn care woker can mow 3 lawns in 60 min. and another can mow 5 lawns in 75 min. How long will it take them to mow 7 lawns together?1 solutions Answer 165251 by josmiceli(9661)   on 2009-09-30 20:18:08 (Show Source): You can put this solution on YOUR website!This is a rate problem In general: (1st worker's rate) + (2nd worker's rate) = (rate working together) given: 1st worker's rate = lawns/min 2nd worker's rate = lawns/min Multiply both sides by min It takes them 1 hr to mow 7 lawns working together
 Equations/219890: i am really struggeling e=wtih my homework. i am in 7th grade and in pre-algebra my question is that i need a algebra equation that EQUALS 29 and only using A,B,C,D EACH ONLY ONCE. A=1 B=2 C=3 D=4 FOR EXAMPLE: (bc)+dxa 2x3=6+4=10x1= 10 so the answer would be 101 solutions Answer 165246 by josmiceli(9661)   on 2009-09-30 20:09:55 (Show Source): You can put this solution on YOUR website!There are probably lots of ways to do this. One way is where Substituting these values: This is the same as OK
 Probability-and-statistics/219887: HOW MANY PEOPLE DO YOU NEED TO GATHER TO BE SURE THAT AT LEAST TWO OF THEM HAVE A BIRTHDAYS IN THE SAME MONHT?1 solutions Answer 165242 by josmiceli(9661)   on 2009-09-30 20:00:50 (Show Source): You can put this solution on YOUR website!The answer is 13 If there are only 12 people, there is a possibility that each has a birthday in a different month
 Linear_Equations_And_Systems_Word_Problems/219874: You have quarters and nickels. You have a total of 15 coins. Altogether you have a total of \$1.55. how many coins do you have?1 solutions Answer 165239 by josmiceli(9661)   on 2009-09-30 19:58:01 (Show Source): You can put this solution on YOUR website!Let = number of nickels Let = number of quarters given: (1) (2) (in cents) --------------------------------- From (1) Subsitute in (2) (2) And You have 11 nickels and 4 quarters
 Mixture_Word_Problems/219575: Hi, I have a solution/miture question. I can solve the problem just fine once I get it in the right order... but this one I'm having a hard time putting all the info where it belongs. Q) A pharmacist has 20L of a 10% drug solution. How many liters of 5% solution must be added to get a mixture that is 8%? If you could just help me get this in the right format I would would be so thankful!! Thanks!!! Casie R1 solutions Answer 165101 by josmiceli(9661)   on 2009-09-30 14:11:31 (Show Source): You can put this solution on YOUR website!Let = liters of 5% solution to be added It doesn't say what the drug is mixed with, so I'll just call it water. In words: (liters of drug in final solution)/(liters of drug + water in final solution) = 8% given: In liters of 10% solution, there is liters of drug In liters of the 5% solution there is liters of drug ------------------------- The Pharmacist must add 13.333 liters of the 5% solution check answer (error due to rounding -OK)
 Expressions-with-variables/219570: A rubber ball is dropped from the height of 13.5 feet. After each bounce the ball only goes up by 60% of what it did on the previous bounce. How high will the ball go after the 38th bounce? I took the 13.5x .6 for the 1st bounce which is 8.1Ft. and the 2nd bounce is 4.9ft. and the third is 2.9ft. I could do this for all the bounces but it would take me forever. How can I write a formula to just put in bounce to get height?1 solutions Answer 165092 by josmiceli(9661)   on 2009-09-30 13:54:37 (Show Source): You can put this solution on YOUR website!I'll try to write a general formula. After the 1st and succeeding bounces, It looks like the formula would be where is the number of bounces and is the height after that bounce After bounces, ft How much is that in millionths of an inch? millionths of inch/ft That looks like billionths of an inch after the 38th bounce
 Probability-and-statistics/219499: A car radiator contains 10 liters of 20% anitfreeze solution. How many liters of pure antifreeze are needed to make the solution 50% antifreeze without replacement?1 solutions Answer 165054 by josmiceli(9661)   on 2009-09-30 11:54:12 (Show Source): You can put this solution on YOUR website!This assumes that the radiator will hold whatever added antifreeze you try to put in. In words: (final liters of antifreeze)/(final liters of total mixture) = 50% Let = liters of antifreeze to be added Multiply both sides by 6 liters of antifreeze needs to be added to make mixture 50% check answer: OK
 Money_Word_Problems/219496: How long does it take your money in your savings account to double at 8% interest rate using the formula A=Pe^rt ? 1 solutions Answer 165052 by josmiceli(9661)   on 2009-09-30 11:45:09 (Show Source): You can put this solution on YOUR website! is the original amount invested. The problem wants to know how long (what is) it takes to make twice this amount, so given: (this is annual intest rate) Divide both sides by Take the natural log of both sides ( is the time in years) I can find years in months also (about 8 months) It takes 8 years and 8 months to double money
 Travel_Word_Problems/219153: how long will it take to drive 50 feet at 25mph?1 solutions Answer 164898 by josmiceli(9661)   on 2009-09-29 19:44:55 (Show Source): You can put this solution on YOUR website!ft = mile mi/hr x ft/mi = ft/hr Set up equation: hrs Note that min/hr x sec/min = sec/hr hrs x sec/hr = sec It will take 1.3636 sec to drive 50 ft
 Numbers_Word_Problems/219202: the sum of two consecutive numbers divided by three equals seventy one? 1 solutions Answer 164893 by josmiceli(9661)   on 2009-09-29 19:35:56 (Show Source): You can put this solution on YOUR website!The consecutive numbers are given: The numbers are 106 and 107 check: OK