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Recent problems solved by 'josmiceli'

josmiceli answered: 9684 problems
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Money_Word_Problems/477400: The student council of Sta. Lucia High School needed 2,500.00 for an annual trip. If five more members joined the group, each members would then save 5.00. How many students planned to make the trip? 1 solutions Answer 327241 by josmiceli(9686)   on 2011-08-03 10:15:56 (Show Source): You can put this solution on YOUR website! Let = number of students who planned to take the trip given: the cost per student is If 5 more joined the group, the cost per student would be ---------------- I can write the equation: Multiply both sides by Using quadratic formula: I can round this to 48 students planned to take the trip check answer: This seems close enough Hope I got it right

Percentage-and-ratio-word-problems/477415: There is a living room suit for $999.99 and I get 20% off. After taking discount I must pay 7% sales tax, what is the total cost for the living room suit with discount and tax? 1 solutions Answer 327229 by josmiceli(9686)   on 2011-08-03 08:30:46 (Show Source): You can put this solution on YOUR website! The final cost is $855.99

Evaluation_Word_Problems/477420: a man can complete a work in 5days another man can do the same work in 8days In how many days can the 2men complete a work? 1 solutions Answer 327228 by josmiceli(9686)   on 2011-08-03 08:23:56 (Show Source): You can put this solution on YOUR website! Add their rates of working Rate of 1st man = ( 1 job ) / ( 5 days ) Rate of 2nd man = ( 1 job ) / ( 8 days ) Let = the number of days that both men working together take to do job --------------- Multiply both sides by They can do the job in just over 3 days

Rate-of-work-word-problems/477326: 4 men take 3 hours to paint a wall. how much time would 6 men take to do the same job? 1 solutions Answer 327203 by josmiceli(9686)   on 2011-08-03 00:48:25 (Show Source): You can put this solution on YOUR website! The rate of working is ( 1 wall ) / (4 hrs) for 4 men Each of the 4 men paints ( 1/4 of a wall) / (4 hrs) That is the same as ( 1 wall ) / ( 16 hrs ) Each of 6 men can paint (1 wall) / (16 hrs) 6 men will take 1/6 of the time to do the same job 6 men will paint ( 1 wall ) / (16/6 hrs) ( 1 wall) / (8/3 hrs) = (1 wall) / (2.6667 hrs) .6667 hrs = 40 min 6 men will take 2 hrs and 40 min to paint the wall

Numbers_Word_Problems/477328: Hi!!!please help me with this one. The tens digit of a certain two - digit number is 4 more than the unit's digit, the sum of the squares of the two digits is 26. Find the numbers. 1 solutions Answer 327202 by josmiceli(9686)   on 2011-08-03 00:36:33 (Show Source): You can put this solution on YOUR website! Let = the units digit Let = the tens digit given: (1) (2) Substitute (1) into (2) (2) (2) (2) (2) (2) (I could see the factors) (Not -5 because minus digits not allowed) and (1) (1) ------------ The number is 51

Rational-functions/477308: Hi. I'm not sure how to start this problem: the absolute value of 2x+1=absolute value of x My computer won't allow me to use the symbols,sorry. 1 solutions Answer 327195 by josmiceli(9686)   on 2011-08-02 23:24:57 (Show Source): You can put this solution on YOUR website! By trial and error, I found that and are solutions. Then, I found that if you square both sides, The squares will be positive no matter what, so I can write The solutions to this are the ones I found. Evidently this is the way to solve the problem

Miscellaneous_Word_Problems/477023: two candles of the same height are lit at the same time. each candle burns at a constant rate and the first candle takes 5 hours while the second candle takes 4 hours to burn completely. find the time, in hours, taken for the height of the first candle to be four time that of the second candle 1 solutions Answer 327061 by josmiceli(9686)   on 2011-08-02 11:00:04 (Show Source): You can put this solution on YOUR website! Let = the height that both candles start at Let = the current height of the 1st candle Let = the current height of the 2nd candle Let = the current time expired in hours given: = the rate of burning of the 1st candle = the rate of burning of the 2nd candle ------------- For the 1st candle: (1) For the 2nd candle: (2) -------------- given: (1) (1) and (2) ------------------------ I can set the right sides equal to each other Divide both sides by Multiply both sides by Multiply both sides by It will take 3 hrs and 45 min for the 1st candle to be 4 times as high as the 2nd candle check answer: Suppose the heights of both start at 1 m For the 1st candle: For the 1st candle: (1) (1) (1) (1) For the 2nd candle: (2) (2) (2) (2) and OK

Money_Word_Problems/477052: Miranda's financial aid stipulates that her tuition not exceed $1500. If her college charges a $90 registration fee pluss $250 per course, What is the greatest number of courses for which Miranda can register? 1 solutions Answer 327055 by josmiceli(9686)   on 2011-08-02 10:17:27 (Show Source): You can put this solution on YOUR website! The most courses she can take is 5, since she can't take a fraction of a course

Linear_Equations_And_Systems_Word_Problems/477048: Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 13% protein ? 1 solutions Answer 327053 by josmiceli(9686)   on 2011-08-02 10:14:18 (Show Source): You can put this solution on YOUR website! Let = pounds of soybean meal needed Let = pounds of cornmeal needed In words: (total pounds of protein in final mixture) / (total pounds in final mixture) = 13% given: = pounds of protein in soybean meal = pounds of protein in cornmeal (1) (2) ----------------------------- Multiply both sides of (2) by (2) Multiply both sides by (2) Divide both sides by (2) Subtract (1) from (2) (2) (1) and, since (1) (1) (1) 200 pounds of soybean meal and 120 pounds of cornmeal need to be mixed check answer: (2) (2) (2) (2) (2) OK

Equations/476962: A number is increased by 50 percent, and then the resulting number is decreased by 40 percent. What was the original number if the final number is eight less than the original? 1 solutions Answer 327011 by josmiceli(9686)   on 2011-08-02 02:44:41 (Show Source): You can put this solution on YOUR website! Let = original number given: is the original number increased by 50% --------------------- is the resulting number decreased by 40% --------------------- The original number was 80 check: Increased by 50% is 120 Decrease this by 40% 120 - .4*120 = 120 - 48 120 - 48 = 72 72 is 8 less than 80 OK

Linear_Equations_And_Systems_Word_Problems/476963: A coffee powder manufacturer works out the variable cost of each kilogram of coffee powder is $2.50 with a fixed cost of $30. He sells it to his distributors at price of $3 per kilogram. a) If the amount of coffee powder is x kg,in the answer sheet, write the cost function (C) and the revenue (R) for the manufacturer. b)What is the breakeven point for the manufacturer? 1 solutions Answer 327009 by josmiceli(9686)   on 2011-08-02 02:32:37 (Show Source): You can put this solution on YOUR website! Let = number of kilograms of coffee powder sold (a) (b) The breakeven point is where kg of coffee powder sold

Age_Word_Problems/476970: John was twice as old as bob last year. In seven years john will be half again as bob. how old are they now? 1 solutions Answer 327001 by josmiceli(9686)   on 2011-08-02 02:07:29 (Show Source): You can put this solution on YOUR website! Let = John's age now Let = Bob's age now given: (1) (2) Note that "half again" means 1.5 times --------------------------------- (1) (1) (1) and (2) (2) (2) -------------------------- Add (1) and (2) (1) (2) Plug this result back into (1) (1) (1) (1) (1) John is 17 now and Bob is 9 now check: (2) (2) (2) (2) OK

Linear_Equations_And_Systems_Word_Problems/476964: A ship travels between two ports. The cost of fuel depends on its speed as follows: C= $100(ax+ b + 10) - x where x is the average speed of the ship in knots (x > 0) and a and b are constants. If the ship travels at 4 knots the cost of fuel is $9000 but at 6 knots it is $7000. a)From two linear equations consist of a and b. b)Find the values of a and b. c)If it speed is 10 knots, what is the cost of the fuel? 1 solutions Answer 326997 by josmiceli(9686)   on 2011-08-02 01:54:19 (Show Source): You can put this solution on YOUR website! given: points (x,C): (4, 9000) (6, 7000) ---------- ---------- Subtract C(4) from C(6) ----------------------------------- Plug this back into So, the equation is: ------------------------- At 10 knots, the cost of fuel is $3,000 ---------------------- Here's a plot where is in knots and is in thousands of dollars

Evaluation_Word_Problems/476875: Hi, I'm stuck on this one word problem, I want to know the steps in order to solve this problem so I am able to do it in the future. I'm currently working on Rational Expressions. Thank you!!! In 3 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 7 minutes. If both belts are used, find how long it takes to move the cans to the storage area. 1 solutions Answer 326949 by josmiceli(9686)   on 2011-08-01 20:49:11 (Show Source): You can put this solution on YOUR website! You need to add their rates of working to get their rate working together For the bigger belt: Rate1 = (300 pounds of aluminum) / (3 minutes) For the smaller belt: Rate2 = (300 pounds of aluminum) / (7 minutes) I will call moving 300 pounds of aluminum 1 job So, Rate1 = and Rate2 = Let = time in minutes for both belts to do this job Rate 1 + rate2 = Rate3 Multiply both sides by min Note that min = 6 sec Working togethers, the belts can move the cans in 2 min and 6 sec

Percentage-and-ratio-word-problems/476651: The total salary of two people is $110,000. One person is paid $45,000 and the other, $65,000. How much more, percentage wise, does the $65,000 person is getting paid over the $45,000? 1 solutions Answer 326825 by josmiceli(9686)   on 2011-08-01 11:32:00 (Show Source): You can put this solution on YOUR website! 44.44 %

Percentage-and-ratio-word-problems/476613: A 3 ounce bottle of vanilla extract costs $0.96 and 9 ounce bottle costs $2.52. What is the difference to the nearest cent between the cost per ounce of the extract in the 3 ounce bottle and the cost per ounce of the extract in the 9 ounce bottle? 1 solutions Answer 326823 by josmiceli(9686)   on 2011-08-01 11:28:28 (Show Source): You can put this solution on YOUR website! cost per ounce of 3 ounce bottle: cost per ounce of 9 ounce bottle: The difference is 4 cents

Numbers_Word_Problems/476570: my tens digit is 3 more than my ones. my hundred digit is 2 less than my tens. im an odd number. 1 solutions Answer 326763 by josmiceli(9686)   on 2011-08-01 04:48:57 (Show Source): You can put this solution on YOUR website! Let = one's digit The number is: If the number is odd, n can only be 1,3,5,7 or 9 If , If , If , If , (this fails, since the 10's digit is not If , (this fails, it's a 4-digit number)

Linear-equations/476446: School Lunch Program: In 1970, 22.4 million students participated in the national school lunch program. By 2000, this number increased to 27.2 million students. (a) Find the slope of the line passing through the points (1970, 22.4) and (2000, 27.2). (b) Interpret the slope as a rate of change. (c) If this tend continues, estimate the number of participants in 2005. 1 solutions Answer 326661 by josmiceli(9686)   on 2011-07-31 19:45:20 (Show Source): You can put this solution on YOUR website! Let = The number of participants, , during year Let for the year 1970 then for the year 2000 ------------------- The equation is ( p is in millions) is the count of participants for 1970 The slope,m, is (change in p) / (change in t) The equation is: ----------------- In 2005: The estimate for 2005 is 28 million students

Age_Word_Problems/476266: 1. If Samantha were three times as old as she was five years ago, she will be sixty less than six times her current age. How old is Samantha? 2. Ryan was born 6 and one-fourth years after Alexander. The sum of their ages is 66 and eleven-twelfth years. How old is Alexander? 3. Samantha is 8 and two-third years older than Jason. The sum of their ages is 23 years. How old is Jason? 1 solutions Answer 326576 by josmiceli(9686)   on 2011-07-31 10:34:06 (Show Source): You can put this solution on YOUR website! Let = Sam's current age = Sam's age 5 years ago = 3 times Sam's age 5 years ago = 60 less than 6 times her current age ------------- (1) Sam is 15 --------- (2) Let Ryan's age now = Let Alex's age now = given: (1) (2) Substitute (1) into (2) (2) (2) (2) (2) Alex is 36 and 7 months ---------------- = Sam's age now = Jason's age now given: (1) (2) -------------- By substitution: (2) (2) (2) (2) Jason is 7 years and 2 months old

Linear-equations/476271: The cost of driving a car includes both fixed costs and mileage costs. Assume that it costs $164.30 per month for insurance and car payments and $0.35 per mile for gasoline, oil, and routine maintenance. (a). Find values for m and b so that y = mx + b models the monthly cost of driving the car x miles. (b). What does the value of b represent? 1 solutions Answer 326569 by josmiceli(9686)   on 2011-07-31 08:41:27 (Show Source): You can put this solution on YOUR website! = miles driven/month = total monthly cost of driving car = all fixed monthly costs that do not depend on the miles driven --------------- given: The equation is:

Percentage-and-ratio-word-problems/476160: The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C=6000/200-2x. So what is the cost to remove 75% of the pollutant? 1 solutions Answer 326531 by josmiceli(9686)   on 2011-07-30 21:53:23 (Show Source): You can put this solution on YOUR website! The cost is 120 million dollars

Linear-equations/476154: I am very lost in this subject and I do need help and plenty of it as I get very flustered to say the least,If someone can help it would be greatly appreciated. With the questions I am about to ask I cam up with (0,5) The question is as follows: 1 Graph equation and identify Y Intercept Y=1/2 x +5 2. Graph by plotting points X=2 3 Graph the equation and plot points Y=1/5x 1 solutions Answer 326528 by josmiceli(9686)   on 2011-07-30 21:48:29 (Show Source): You can put this solution on YOUR website! Think of the equation as a long series of points that make up a straight line. The straight line and the equation are the same thing. The convention for showing a point is: (x,y) You need both an x and a y to be a point, but they must be points on this line. You can determine the points this way: (0,?) (1,?) (2,?) (3,?) (4,?) (5,?) etc. Or, this way: (?,0) (?,1) (?,2) (?,3) (?,4) (?,5) etc. So, given the x or y, you can find the point that falls on the line. --------------- The y-intercept occurs where is the y-intercept The graph is: ---------------------------- This just says: No matter what number I choose for y, I will alway have . The points on this line will look like: (2,y), and y can be any number. This is plotted as a vertical line --------------------------

Evaluation_Word_Problems/476065: Can you Help me Please with this question ! THANKYOU ! Geologists estimate that the continents of Europe and North America are drifting apart at a rate of an average of 12 miles every 1 million years, or about 0.75 inch per year. If the continents continue to drift apart at that rate, how many inches will they drift in 50 years? 1 solutions Answer 326475 by josmiceli(9686)   on 2011-07-30 15:46:25 (Show Source): You can put this solution on YOUR website! in/yr x yr = 37.5 in

test/476077: How can we use logarism in base ten? 1 solutions Answer 326473 by josmiceli(9686)   on 2011-07-30 15:43:30 (Show Source): You can put this solution on YOUR website! A logarithm is an exponent In the equation , is the log and is the base. If the base is , I write I can rewrite this as: This is read as: The log to the base 10 which gives me is ----------------- As an example, I have , and find Solving on my calculator, , or

Travel_Word_Problems/476024: A bus entered the Interstate and traveled at a constant speed of 42 mph. Two hours later a second bus followed the first bus, entering the Interstate from the same point as the first bus, and traveled at a constant speed of 66 mph. How long will it take the second bus to catch up with the first bus? 1 solutions Answer 326444 by josmiceli(9686)   on 2011-07-30 12:43:05 (Show Source): You can put this solution on YOUR website! How many miles head start does the 1st bus have? mi Start a stopwatch when the 2nd bus enters interstate. Both will now travel for the same amount of time until bus 2 catches bus 1. Call this time . --------------------- Let = distance bus 2 has to go to catch bus 1 For bus 2: (2) For bus 1: (1) ---------------- Substitute in (2) for in (1) (1) (1) (1) It takes the 2nd bus 3.5 hrs to catch 1st bus check: (2) (2) (2) and (1) (1) (1) OK

Geometry_Word_Problems/476014: A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their area is 28 square feet, find the length of the sides of the poster and the sign. 1 solutions Answer 326438 by josmiceli(9686)   on 2011-07-30 12:09:28 (Show Source): You can put this solution on YOUR website! Let a side of the square sign = ft The area of the square sign = ft2 given: A side of the square poster = ft The area of the square poster = ft2 ft2 A side of the square sign is 8 ft A side of the square poster is 6 ft check answer: OK

Linear_Equations_And_Systems_Word_Problems/476000: A gas station owner has 30 gallons of gasoline for which he charges $3.03 per gallon and some for which he charges $3.74 per gallon. How many gallons of the $3.74 brand must the owner mix in to produce gasoline that costs $3.28 per gallon? 1 solutions Answer 326435 by josmiceli(9686)   on 2011-07-30 11:48:23 (Show Source): You can put this solution on YOUR website! Let = gallons of $3.74 gas to be mixed in In words: ( cost of $3.03 gas ) + ( cost of $3.74 gas ) = ( cost of $3.28 gas ) given: Cost of $3.03 gas = Cost of $3.74 gas = Cost of $3.28 gas = -------------------------------- The owner must mix in 16.304 gallons of the $3.74 gas check answer: OK

Age_Word_Problems/476006: Karen is eleven years less than four times John’s age. If Karen is 49, how old is John? 1 solutions Answer 326433 by josmiceli(9686)   on 2011-07-30 11:30:11 (Show Source): You can put this solution on YOUR website! Let = Johns age Let = Karen's age given: ------------ John is 15 yrs old

Linear_Equations_And_Systems_Word_Problems/476003: Lisa invested $8000, part at 4% and the rest at 5% per year. How much did she invest at each rate if her total return per year on the investments was $380? 1 solutions Answer 326432 by josmiceli(9686)   on 2011-07-30 11:26:25 (Show Source): You can put this solution on YOUR website! Let = amount invested @ 4% per yr Let = amount invested @ 5% per yr given: (1) (2) ---------------------- (2) Multiply both sides of (1) by and subtract from (2) (2) (1) and (1) (1) (1) $2,000 is invested @ 4% per yr $6,000 is invested @ 5% per yr

Polynomials-and-rational-expressions/475872: The equation x⁴-2x²-16x-15 has four roots. If two of the roots are real and equal to x=-1 and x=3, by a process of long division and solving a quadratic equation find the two complex roots 1 solutions Answer 326414 by josmiceli(9686)   on 2011-07-30 06:40:45 (Show Source): You can put this solution on YOUR website! given: and -------------- Complex roots come in pairs of the form and I can factor out I can use quadratic formula now 1st root and 2nd root

Percentage-and-ratio-word-problems/475944: A crew consists of 1 apprentice, 1 journeyman, and 1 master carpenter. The crew receives a check for $5100 for a job they finished. A journeyman makes 300% of what an apprentice makes and a master carpenter makes make 150% of what a journeyman makes. How much does each person on the crew earn? 1 solutions Answer 326413 by josmiceli(9686)   on 2011-07-30 06:21:14 (Show Source): You can put this solution on YOUR website! Let = apprentices earnings Let = journeyman's earnings Let = master carpenter's earnings given: (1) (2) (3) This is 3 equations and 3 unknowns, so it's solvable ------------------- (2) (2) Substitute (2) and (3) into (1) (1) (1) Multiply both sides by (1) (1) (1) and, (2) (2) and, (3) (3) (3) $600 = apprentices earnings $1800 = journeyman's earnings $2700 = master carpenter's earnings check: OK