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# Recent problems solved by 'josmiceli'

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 Percentage-and-ratio-word-problems/373440: carlos worked 31.5 hours at a hospital as a volunteer. this represents 87.5% of his schools requirement for community service. how many hours does his school require for community service1 solutions Answer 265789 by josmiceli(9649)   on 2010-11-18 20:45:32 (Show Source): You can put this solution on YOUR website!Let = his school's requirement for community service 36 hours is the requirement
 Mixture_Word_Problems/373434: \$9500 is invested, part of it at 10% and part of it at 8%. For a certain year, the total yield is \$878.00. How much was invested at each rate? How much was invested at 10%? How much was invested at 8%?1 solutions Answer 265786 by josmiceli(9649)   on 2010-11-18 20:41:08 (Show Source): You can put this solution on YOUR website!Let = amount invested at 10% Let = amount invested at 8% given: (1) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) \$5,900 was invested at 10% and \$3,600 was invested at 8% check answer: OK
 Word_Problems_With_Coins/373028: if i have 20 coins only dimes and quarters and have \$3.80 how many quters do i have1 solutions Answer 265613 by josmiceli(9649)   on 2010-11-18 02:24:14 (Show Source): You can put this solution on YOUR website!Let = number of dimes Let = number of quarters given: (1) (2) (in cents) ------------------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) And, from (1), I have 8 dimes and 12 quarters check answer: (2) (2) OK
 Equations/373047: one canned juice drink is 20% orange juice; another is 5% orange juice. how many liters of each should be mixed together in order to get 15L that is 13% orange juice?1 solutions Answer 265611 by josmiceli(9649)   on 2010-11-18 02:16:57 (Show Source): You can put this solution on YOUR website!Let = liters of 20% oj needed Let = liters of 5% oj needed given: (1) (2) ------------------------------------- From (2): (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) And, from (1), 8 liters of 20% oj and 7 liters of 5% oj are needed check the answer: (2) OK
 Quadratic_Equations/372841: I have pulled my hair out trying to learn this stuff!! If anyone could help me I'd so appreciate it!! thank you!! Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 3x + 11y = 34.5 9x – 7y = -16.51 solutions Answer 265538 by josmiceli(9649)   on 2010-11-17 19:38:17 (Show Source): You can put this solution on YOUR website!It helps to get all the terminology straight, otherwise, you can't talk about it You have: 1st equation: (term 1) + (term 2) = (term 3) 2nd equation: (term 1) + (term 2) = (term 3) What you are trying to do is get either the (term 1)'s equal to each other or the (term 2)'s equal to each other. Then the next step is to multiply both sides of equation 2 by -1 Then when add the equations, you get: 1st equation: (term 1) + (term 2) = (term 3) 2nd equation: -(term 1) - (term 2) = -(term 3) So, you've gotten rid of either the (term 1)'s or the (term 2)'s -------------- How do you get (term 1)'s equal to each other? Multiply both sides of equation 1 by Now you can multiply both sides of equation 2 by and add the equations (note that all the signs are changed) Adding: Divide both sides by Now you can plug this result back into either equation and find Does this help?
 Percentage-and-ratio-word-problems/372817: the animal shelter has only dogs and cat's. there are 25% more dogs than cats. what percentage of the animals at the animal shelter are cats? explain your solution1 solutions Answer 265533 by josmiceli(9649)   on 2010-11-17 19:16:22 (Show Source): You can put this solution on YOUR website!Let = number of dogs Let = number of cats given: The percentage of animals that are cats = By substitution: The cats are 44.44% of the animals check: If there were 125 dogs,
 Equations/372821: 4 1/6 = r + 6 1/4 i got 1 12/13 is that right?1 solutions Answer 265529 by josmiceli(9649)   on 2010-11-17 19:02:47 (Show Source): You can put this solution on YOUR website!Get fractions in terms of 1/12's 4 2/12 = r + 6 3/12 check answer: = -2 1/12 4 2/12 = r + 6 3/12 4 2/12 = -2 1/12 + 6 3/12 4 + 2 - 6 = 3/12 - 1/12 - 2/12 0 = 3/12 - 3/12 0 = 0 OK
 Finance/372802: A car rental company charges a daily rental fee plus a per mile fee over 150 miles. Two different people rent the same style of car for the same number of days. The total bill for one persons rental is \$207.50 for a 5-day rental and 180 miles. The total bill for the other persons rental is \$212.50 for a 5-day rental and 200 miles. I need to write a linear system that I can use to find the daily rental fee and the per mile fee over 150 miles.1 solutions Answer 265527 by josmiceli(9649)   on 2010-11-17 18:53:57 (Show Source): You can put this solution on YOUR website!Let = daily rental fee Let = the per mile fee over 150 miles given: Person 1: cost of daily rental = Person 2: cost of daily rental = Person 1: per mile fee over 150 miles = Person 2: per mile fee over 150 miles = ------------------ Multiply both sides of each equation by Divide both sides of each equation by
 Systems-of-equations/372765: A dehydrated patient needs a 2.6% saline IV. Unfortunately, the hospital only has bags of 8% and 2% saline solutions. How many liters of each solutions should be mixed together to yield 2 liters of the desired concentration.1 solutions Answer 265514 by josmiceli(9649)   on 2010-11-17 18:20:20 (Show Source): You can put this solution on YOUR website!Let = liters of 8% solution needed Let = liters of 2% solution needed In words: (liters of saline)/(liters of solution) = 2.6% (1) (2) ------------------ From (1): (1) (1) Multiply both sides of (2) by and subtract from (1) (1) (2) And, since .2 liters of 8% solution and 1.8 liters of 2% solution are needed check answer: (1) (1) (1) OK
 Complex_Numbers/372780: What is the complex conjugate of the (square root of -400) + 17?1 solutions Answer 265511 by josmiceli(9649)   on 2010-11-17 18:02:02 (Show Source): You can put this solution on YOUR website!The complex conjugate of =
 test/368101: A fish was caught whose tail weighed 9 lb. Its head weighed as much as it's tail pluse half its body. Its body weighed as much as it's head and tail. What did the fish weigh?1 solutions Answer 262328 by josmiceli(9649)   on 2010-11-08 19:51:38 (Show Source): You can put this solution on YOUR website!Let = weight of tail Let = weight of body Let = weight of head given: --------------- By substitution: (1) and (2) Subtract (2) from (1) (1) (2) And, since, The fish weighed pounds check answer: and OK
 Numeric_Fractions/367722: What is 3 2/3 over 7/5 = 3/7 over x?1 solutions Answer 262125 by josmiceli(9649)   on 2010-11-08 11:39:19 (Show Source):
 Quadratic_Equations/367310: solve 1 solutions Answer 261819 by josmiceli(9649)   on 2010-11-07 16:23:07 (Show Source): You can put this solution on YOUR website! Let Take the zth root of both sides Since ,
 Exponents-negative-and-fractional/367300: How do I solve 81^-3/41 solutions Answer 261814 by josmiceli(9649)   on 2010-11-07 16:12:44 (Show Source): You can put this solution on YOUR website! Note that Rewrite the problem as: I can rewrite this as: This equals
 Travel_Word_Problems/367292: Two joggers are running around an oval track in opposite directions. One jogger runs around the track in 56 seconds. They meet every 24 seconds. How mant seconds does it take the second jogger to run around the track?1 solutions Answer 261810 by josmiceli(9649)   on 2010-11-07 16:03:58 (Show Source): You can put this solution on YOUR website!Each jogger cuts down the distance between them as they jog. They are always approaching each other at their combined speeds Jogger #1 has a speed of (1 trip around)/56 sec At the sum of their speeds, (1 trip around)/24 sec Let = speed of Jogger #2 Multiply both sides by The 2nd Jogger takes 42 sec to go around track
 Quadratic_Equations/366861: The number of tickets sold each day for an upcoming performance of handel's Messiah is givn by N(x)=-0.4x^2+10.4x+10 where x is the number of days since the concert was first announced. When will daily sales peak and how many tickets will be sold that day? Pleas show work Thank you1 solutions Answer 261552 by josmiceli(9649)   on 2010-11-06 17:51:08 (Show Source): You can put this solution on YOUR website! The peak is at when the equation is in the form Sales will peak 13 days after concert is announced Solve for
 Age_Word_Problems/366640: Erica and Rachel are both 90 years old. Breena, on the other hand, is half again as old as she was when she was half again as old as she was when she lacked five years of being half as old as she is now. How old is Breena?1 solutions Answer 261451 by josmiceli(9649)   on 2010-11-06 07:51:08 (Show Source): You can put this solution on YOUR website!Let = her age now = half as old as she is now = lacking 5 years of being half as old as she is now = half again as old as she was when she lacked five years of being half as old as she is now. = half again as old as she was when she was half again as old as she was when she lacked five years of being half as old as she is now. She is this age now, so Breena is 90 also
 Quadratic_Equations/366783: What is the distance between the points where the graph of y = - 2x^2 - x + 15 crosses the x-axis?1 solutions Answer 261450 by josmiceli(9649)   on 2010-11-06 07:32:14 (Show Source): You can put this solution on YOUR website! Find the roots, which are the x-axis crossings. Use quadratic formula and The difference between the roots is Here's the plot:
 Quadratic_Equations/366752: please help me find the find real solution to 1 solutions Answer 261417 by josmiceli(9649)   on 2010-11-06 01:29:57 (Show Source): You can put this solution on YOUR website! Use quadratic formula and And since , These are the real solutions gives 2 imaginary solutions
 Radicals/366749: please help me find the real solution of this equation 1 solutions Answer 261414 by josmiceli(9649)   on 2010-11-06 01:19:18 (Show Source): You can put this solution on YOUR website! Subtract from both sides Square both sides Take the square root of both sides and This only works if the square root is negative) The real solution is x = 4
 Quadratic-relations-and-conic-sections/366722: Write the equation for the parabola which opens left, has its vertex on the origin, and passes through the point (-3/2),1)1 solutions Answer 261412 by josmiceli(9649)   on 2010-11-06 01:10:12 (Show Source): You can put this solution on YOUR website!It would be of the form If the vertex is at the origin, then I can write , so If it includes (-3/2,1), (1) By symmetry, it must also pass through (-3/2,-1), so (2) Add (1) and (2) And, since (1) The equation is
 Graphs/366748: find the slope is it exists 5x-6y=121 solutions Answer 261410 by josmiceli(9649)   on 2010-11-06 00:56:17 (Show Source): You can put this solution on YOUR website!Get it into the form where is the slope Add to both sides Subtract from both sides Divide both sides by The slope is 5/6
 Miscellaneous_Word_Problems/366609: Find the slope if it exists, of the line containing the points [-1 1/2] and [-10 1/2]1 solutions Answer 261276 by josmiceli(9649)   on 2010-11-05 16:18:01 (Show Source): You can put this solution on YOUR website!The points are in the format (x1,y1) and (x2,y2). Notice that y1 = 1/2 and y2 = 1/2 If there is no change in y for any 2 points on a line, then that line has to be vertical, or slope = infinity the equation of the line is
 Polynomials-and-rational-expressions/366571: Choose two trinomials from the list below to factor. Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation. 2x2 + 13x + 15 2x2 + 27x + 13 5x2 − 2x − 7 10x2 − 7x − 3 8x2 − 11x + 3 HELP PLEASE??1 solutions Answer 261275 by josmiceli(9649)   on 2010-11-05 16:13:44 (Show Source): You can put this solution on YOUR website!The second one, , can be solved by careful inspection. First I notice that . I want to arrange the factors so I get this result for the coefficient of accomplishes this. --------------------------- For the 4th one, , I try and for the factors of . Then I try and for the factors of . This gives me as the answer with as the coefficient of
 Mixture_Word_Problems/366493: Soybean meal is 14% protein; cormeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 11% protein? How many pounds of the cornmeal should be in the mixture? How many pounds of the soybean meal should be in the mixture?1 solutions Answer 261168 by josmiceli(9649)   on 2010-11-05 09:57:25 (Show Source): You can put this solution on YOUR website!Let = pounds of cornmeal needed Let = pounds of soybean meal needed given: Pounds of protein in pounds of cornmeal: Pounds of protein in pounds of soybean meal (1) ---------------- In words: (pounds of protein in final mixture)/(total pounds of final mixture) = 11% divide both sides by (2) Subtract (1) from () (2) (1) and, since 120 pounds of cornmeal and 160 pounds of soybean meal are needed check answer: OK
 Miscellaneous_Word_Problems/366383: A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 120 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 6% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?1 solutions Answer 261079 by josmiceli(9649)   on 2010-11-04 22:33:01 (Show Source): You can put this solution on YOUR website!Let = gallons of 4% solution to be drained given: Bleach in 4% solution: gal Bleach in removed portion: Gallons of bleach added: ---------- In words: (initial gallons of bleach - bleach removed + bleach added)/(total gallons) = 6% 2.5 gallons of 4% solution must be drained and replaced with pure bleach
 Numbers_Word_Problems/366367: I am a number between 70 and 100. My ones digit is 1 more than my tens digit. I am a prime number. What number am I?1 solutions Answer 261068 by josmiceli(9649)   on 2010-11-04 21:56:50 (Show Source): You can put this solution on YOUR website!I can eliminate 70, 100, 99, and 98, which all have divisors So I'm left with 71 through 97 I can eliminate all numbers ending in 2,4,5,6, and 8, since they all have divisors. That leaves number ending in 1,3,7, or 9 The tens digit has to be 7,8, or 9. If the ones digit is 1 more than the tens digit, then the possible numbers are just one: 89
 Word_Problems_With_Coins/366373: Luis and Julia have the same number of coins. Luis has only dimes and Julia has only quaters. If Julia has \$1.80 more than Luis does, how many coins do each have ?1 solutions Answer 261061 by josmiceli(9649)   on 2010-11-04 21:44:59 (Show Source): You can put this solution on YOUR website! (in cents) By substitution: Each has 12 coins
 Travel_Word_Problems/366347: a car travels down the highway at 60km/hr for2.5hours .How far has the car gone?1 solutions Answer 261053 by josmiceli(9649)   on 2010-11-04 21:28:04 (Show Source): You can put this solution on YOUR website! The car went 150 km
 Money_Word_Problems/366356: If you spent \$78.00 on clothing and the sales tax was 4.5%, how much change should you get from \$100.00?1 solutions Answer 261050 by josmiceli(9649)   on 2010-11-04 21:26:20 (Show Source): You can put this solution on YOUR website! You should get \$18.49 change
 Linear-equations/366319: Translate to an equation: f \$50 poker chips and t \$20 poker chips total \$400 Determine three different combinations of \$50 poker chips and \$20 poker chips that total \$4001 solutions Answer 261044 by josmiceli(9649)   on 2010-11-04 21:22:47 (Show Source): You can put this solution on YOUR website! since if , there are no \$20 chips Suppose -can't have 1/2 a chip ----------- Suppose ------------ Suppose ------------ Suppose