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Recent problems solved by 'stanbon'

stanbon answered: 57894 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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Numbers_Word_Problems/532691: Half the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 3. Find the numbers. 1 solutions Answer 350900 by stanbon(57967)   on 2011-11-16 14:22:42 (Show Source): You can put this solution on YOUR website! Half the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 3. Find the numbers. ----- (1/2)(x-y) = 2 x + 2y = 3 ----- Modify: x - y = 4 x + 2y= 3 ----- subtract and solve for "y": 3y = -1 y = -1/3 ---- Solve for "x": x = y+4 x = 3 2/3 ================= Cheers, Stan H. ===============

Problems-with-consecutive-odd-even-integers/532684: Find two consecutive odd integers, given the first odd integer is x. 1 solutions Answer 350899 by stanbon(57967)   on 2011-11-16 13:56:38 (Show Source): You can put this solution on YOUR website! Find two consecutive odd integers, given the first odd integer is x. If "x" is the 1st "x+2" would be the next consecutive. --- However, odd integers are all 1 more or 1 less than even integers, and even integers are always a multiple of 2. --- So the way to symbolize 2 consecutive odd integers could be 2x-1,2x+1 --- or ---- 2x+1, 2x+3 --- etc. Cheers, Stan H. ===============

Quadratic-relations-and-conic-sections/532680: please explain to me in the simplest way possible how to determine the area of an ellipse 1 solutions Answer 350898 by stanbon(57967)   on 2011-11-16 13:52:57 (Show Source): You can put this solution on YOUR website! Use Google to search for "area of an ellipse" Here is one of the sites listed. Cheers, Stan H. -------------- http://www.math.hmc.edu/funfacts/ffiles/10006.3.shtml

Probability-and-statistics/532494: jake and jessica are working on a problem jake has a 45% chance of solving it, and jessica a 65% chance. find the probability that both solve the problem? 1 solutions Answer 350897 by stanbon(57967)   on 2011-11-16 13:01:31 (Show Source): You can put this solution on YOUR website! jake and jessica are working on a problem jake has a 45% chance of solving it, and jessica a 65% chance. find the probability that both solve the problem? --- Ans: 0.45*0.65 ================ Cheers, Stan H.

Probability-and-statistics/532664: Approximately 8% of people are left-handed. If two people are selected at random, what is the probability of the following events? A. P(Both are right-handed) = B. P(Both are left-handed) = C. P(One is right-handed and the other is left-handed) = D. P(At least one is right-handed) = 1 solutions Answer 350896 by stanbon(57967)   on 2011-11-16 12:56:19 (Show Source): You can put this solution on YOUR website! duplicate

Probability-and-statistics/532665: Approximately 8% of people are left-handed. If two people are selected at random, what is the probability of the following events? A. P(Both are right-handed) = B. P(Both are left-handed) = C. P(One is right-handed and the other is left-handed) = D. P(At least one is right-handed) = 1 solutions Answer 350895 by stanbon(57967)   on 2011-11-16 12:55:40 (Show Source): You can put this solution on YOUR website! Approximately 8% of people are left-handed. If two people are selected at random, what is the probability of the following events? A. P(Both are right-handed) = (0.92)^2 ------ B. P(Both are left-handed) = (0.08)^2 ------------ C. P(One is right-handed and the other is left-handed) = 1 -[0.92^2+0.08^2] ----------------------- D. P(At least one is right-handed) = 1 - 0.08^2 ================================= Cheers, Stan H.

Mixture_Word_Problems/532666: The speed of a stream is 5 mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 miles upstream, what is the speed of the boat in still water? 1 solutions Answer 350894 by stanbon(57967)   on 2011-11-16 12:52:44 (Show Source): You can put this solution on YOUR website! The speed of a stream is 5 mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 miles upstream, what is the speed of the boat in still water? ---- Downstream DATA: distance = 72 miles ; rate = b+5 mph ; time = 72/(b+5) hrs. ---- Upstream DATA: distance = 36 miles ; rate = b-5 mph ; time = 36/(b-5) hrs ---- Equation: time = time 72(b+5) = 36/(b-5) ------- 2/(b+5) = 1/(b-5) Cross-multiply to get: 2b-10 = b+5 b = 15 mph (speed of the boat in still water) =================== Cheers, Stan H. ===================

Functions/532597: what is the domain and range of the function f(x)=sqrt(x-7) 1 solutions Answer 350878 by stanbon(57967)   on 2011-11-16 10:48:07 (Show Source): You can put this solution on YOUR website! what is the domain and range of the function f(x)=sqrt(x-7) ------------------- Domain: x-7 must be >= 0 x >- 7 is the domain. So, domain is All Real Numbers >= 7 ----- Range: sqrt(x-7) must be >= 0 So, range is All Real Numbers >= 0 ======================================== Cheers, Stan H. =============

test/532607: |-3x+2|+4>14 1 solutions Answer 350875 by stanbon(57967)   on 2011-11-16 10:33:30 (Show Source): You can put this solution on YOUR website! |-3x+2|+4 > 14 ------ |-3x+2| > 10 ------ -3x+2 < -19 or -3x+2 > 10 ------ -3x < -21 or -3x > 8 ------ x > 7 or x < -8/3 ====================== Cheers, Stan H. ======================

Probability-and-statistics/532496: how do i draw a tree diagram to find the number of possible outcomes for each situation {this is the question} how many outcomes are possible if the 0-5 number cube is rolled and the spinner is spun? (The numbers on the spinner are 1,2,4,3) 1 solutions Answer 350874 by stanbon(57967)   on 2011-11-16 10:02:28 (Show Source): You can put this solution on YOUR website! how do i draw a tree diagram to find the number of possible outcomes for each situation {this is the question} how many outcomes are possible if the 0-5 number cube is rolled and the spinner is spun? (The numbers on the spinner are 1,2,4,3) ---- Let left-most column be 0,1,2,3,4,5 --- To the right put a column which lists 1,2,3,4 to the right of EACH of the elements in the 1st column ---- You should end up with 6*4 = 24 branches ======================================== Cheers, Stan H.

Probability-and-statistics/532593: An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probalitiy that there is a least one correct answer. 1 solutions Answer 350872 by stanbon(57967)   on 2011-11-16 09:53:02 (Show Source): You can put this solution on YOUR website! An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probalitiy that there is a least one correct answer. ----- P(1<= x <=10) = 1 - P(x = 0) ------- P(at least one correct) = 1 - 10C0*(1/2)^0*(1/2)^10 = 1- (1/1024) ------------------------------- Cheers, Stan H. ===================

Probability-and-statistics/532545: Suppose you have 7 types of cereal. If you eat a bowl of cereal every morning for breakfast, how many ways can you eat breakfast in the next 4 days? 1 solutions Answer 350871 by stanbon(57967)   on 2011-11-16 09:49:48 (Show Source): You can put this solution on YOUR website! Suppose you have 7 types of cereal. If you eat a bowl of cereal every morning for breakfast, how many ways can you eat breakfast in the next 4 days? --- 1st day: 7 choices 2nd day: 6 choices 3rd day: 5 choices 4th day: 4 choices ----- Ans: 7P4 = 7!/3! = 42*20 = 840 ================================== Cheers, Stan H. =========

Probability-and-statistics/532587: a batch consists of 12 defective coils and 88 good ones. find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made. 1 solutions Answer 350870 by stanbon(57967)   on 2011-11-16 09:45:46 (Show Source): You can put this solution on YOUR website! a batch consists of 12 defective coils and 88 good ones. find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made. --- Binomial Problem with n = 2 and p(good) = 0.88 ---- P(x = 2) = 2C2*(0.88)^2*(0.12)^0 = 0.88^2 -------- Cheers, Stan H. ===========

Radicals/532586: how do you solve (2radical3-5)raised to the 2nd power??? 1 solutions Answer 350869 by stanbon(57967)   on 2011-11-16 09:42:40 (Show Source): You can put this solution on YOUR website! (2radical3-5)raised to the 2nd power??? --------- (2sqrt(3) - 5)(2sqrt(3) - 5) --- Use FOIL: F: 4*3 = 12 O: -10sqrt(3) I: -10sqrt(3) L: 25 ---- Combine to get: = 37 - 20sqrt(3) ===================== Cheers, Stan H.

Linear-equations/532579: Hello! Please help me solve the following question, I honestly am so confused about how to solve it=( Write the point-slope form of an equation of the line that passes through (-2, 5) and has a slope of zero. I was thinking it may be -2x+5y=0 Thank you! 1 solutions Answer 350868 by stanbon(57967)   on 2011-11-16 09:39:49 (Show Source): You can put this solution on YOUR website! Write the point-slope form of an equation of the line that passes through (-2, 5) and has a slope of zero. ---- You are given y = 5 when x = -2 and you are given m = 0 ---- Equation Form is y = mx + b Solve for "b": 5 = 0*-2 + b b = 5 ----- Equation: y = 0*x + 5 --- Ans: y = 5 ========================== Cheers, Stan H.

Radicals/532580: My homework says to rationalize the denominator. I've tried another problem similar to this and I ended up getting it wrong. This is another one I'm stuck on. Cube root of 35 over the cube root of 21. I thought you had to break the top as cube roots of 5 and 7 and break the bottom as cube roots of 3 and 7 and cancel out, then multiply the top and bottom by the cube root of three. Is that the correct way to rationalize? Please and thank you! 1 solutions Answer 350867 by stanbon(57967)   on 2011-11-16 09:36:50 (Show Source): You can put this solution on YOUR website! Cube root of 35 over the cube root of 21 ------ Multiply numerator and denomator by cbrt(21^2) to get: ---- = cbrt(35*21^2)/cbrt(21^3) ---- = cbrt(7^3*5*3^2)/21 ---- = (7/21)*cbrt(45) --- = (1/3)cbrt(45) ================== Cheers, Stan H. ==================

Probability-and-statistics/532380: Decide whether the experiment is a binomial experiment. If it is not, explain why. You spin a number wheel that has 10 numbers 100 times. The random variable represents the winning numbers on each spin of the wheel. 1 solutions Answer 350834 by stanbon(57967)   on 2011-11-15 22:13:51 (Show Source): You can put this solution on YOUR website! Decide whether the experiment is a binomial experiment. If it is not, explain why. You spin a number wheel that has 10 numbers 100 times. The random variable represents the winning numbers on each spin of the wheel. -------- No; the probability of success is not the same on each trial. Cheers, Stan H. ================

Mixture_Word_Problems/532395: a pharmascist has a 40% acid solution and a 25% acid solution. How many liters of each must be mixed to form 147 liters of a 34% acid solution? 1 solutions Answer 350832 by stanbon(57967)   on 2011-11-15 22:09:59 (Show Source): You can put this solution on YOUR website! A pharmacist has a 40% acid solution and a 25% acid solution. How many liters of each must be mixed to form 147 liters of a 34% acid solution? ------------------------ Equation: acid + acid = acid 0.40x + 0.25(147-x) = 0.34*147 ---- Multiply thru by 100 to get: 40x + 25*147 - 25x = 34*147 ---- 15x = 9*147 x = (3/5)(147) x = 88.2 liters (amt. of 40% solution needed) 147-x = 58.8 liters (amt. of 25% solution needed) ==================================================== Cheers, Stan H. =====================

Travel_Word_Problems/532390: Ellen and Kate raced on their bicycles to the library after school. They both left school at 3:oo p.m. and bicycled along the same path. Ellen rode at a speed of 12 miles per hour and kate rode at 9 miles per hour. Ellen got to the library 15 minutes before kate. How long did it take Ellen to get to the library? At what time did Ellen get to the library? 1 solutions Answer 350831 by stanbon(57967)   on 2011-11-15 22:03:39 (Show Source): You can put this solution on YOUR website! Ellen and Kate raced on their bicycles to the library after school. They both left school at 3:oo p.m. and bicycled along the same path. Ellen rode at a speed of 12 miles per hour and kate rode at 9 miles per hour. Ellen DATA: rate = 12 mph ; time = x hrs ; distance = 12x miles --- Kate DATA: rate = 9 mph ; time = x + 1/4 hrs ; distance = 9(x+(1/4)) miles ------------------------------- Ellen got to the library 15 minutes before kate. How long did it take Ellen to get to the library? At what time did Ellen get to the library? ====== Equation: distance = distance: 12x = 9x + 9/4 3x = 9/4 x = 3/4 hr (Ellen's time) She arrived at the library at 4:00 ---------- x + (1/4) = 1 hr (Kate's time) =================================== Cheers, Stan H. ================

Triangles/532385: the lengths of a triangle are 3 inches and 8 inches. Find the range of possible lengths for the third side, s. 1 solutions Answer 350828 by stanbon(57967)   on 2011-11-15 21:54:38 (Show Source): You can put this solution on YOUR website! the lengths of a triangle are 3 inches and 8 inches. Find the range of possible lengths for the third side, s. s < 3+8 ----- s > 8-3 ============== Cheers, Stan H.

Exponential-and-logarithmic-functions/532366: I am not sure how to answer this 9^x-3^(x+1)+1=0 1 solutions Answer 350821 by stanbon(57967)   on 2011-11-15 21:39:03 (Show Source): You can put this solution on YOUR website! I am not sure how to answer this 9^x-3^(x+1)+1=0 ------ (3^x)^2 - 3^x*3 + 1 = 0 --- (3^x)^2 - 3(3^x) + 1 = 0 ---- Let w = 3^x: w^2 - 3w + 1 = 0 ---- w = [3 +- sqrt(9-4*1*1)]/2 ---- w = [3 +- sqrt(5)]/2 ---- w = (3/2)+(1/2)sqrt(5) or w = (3/2)-(1/2)sqrt(5) ---- Solve for "x" 3^x = (3/2)+(1/2)sqrt(5) or 3^x = (3/2)-(1/2)sqrt(5) ----- x = ln[(3/2)+sqrt(5)/2}/ln(3) or x = ln[(3/2)-(sqrt(5)/2)/ln(3) ================================= Cheers, Stan H. ====================

Circles/532362: The diameter of a circle connects two points(2,-3)and(6,4)on the circle.Find the coordinates of the center of the circle 1 solutions Answer 350818 by stanbon(57967)   on 2011-11-15 21:31:00 (Show Source): You can put this solution on YOUR website! The diameter of a circle connects two points(2,-3)and(6,4)on the circle.Find the coordinates of the center of the circle. ------------ Find the midpoint: (x,y) --- x = (2+6)/2 = 4 y = (-3+4)/2 = 1/2 ------ center = (4,1/2) ==================== Cheers, Stan H. ====================

Probability-and-statistics/532360: You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places. 1 solutions Answer 350816 by stanbon(57967)   on 2011-11-15 21:28:27 (Show Source): You can put this solution on YOUR website! You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places. ---- P(2 then 10) = (4/52)(4/51) = 0.006 ======================================= Cheers, Stan H. ===============

Exponential-and-logarithmic-functions/532358: is the answer to 2^(x+1)=5^(1-2x) x=(ln 2+ln 5)/(ln 2-5ln2)? 1 solutions Answer 350815 by stanbon(57967)   on 2011-11-15 21:25:57 (Show Source): You can put this solution on YOUR website! is the answer to 2^(x+1)=5^(1-2x) x=(ln 2+ln 5)/(ln 2-5ln2)? ----------------------------------- 2^(x+1)=5^(1-2x) (x+1)*ln(2) = (1-2x)*ln(5) -------- x*ln(2) + ln(2) = ln(5) -2ln(5)x ------ Get the "x" terms together. ------- x (ln(2)+2ln(5)) = ln(5)-ln(2) --- x(ln[2*25)) = ln(5/2) --- x = ln(5/2)/ln(50) --- x = 0.2342 ================ Cheers, Stan H. ================

Geometric_formulas/532355: Please help, I am having so much trouble in this class. construct a frequency distribution with a first class (in ten thousands) of 157–234. Magazine Circulation (ten thousands) Reader’s Digest 1001 Better Homes & Gardens 761 TV Guide 735 National Geographic 538 Good Housekeeping 466 Family Circle 429 Ladies’ Home Journal 411 Woman’s Day 409 TIME 403 People 369 AAA Westways 368 Prevention 335 Sports Illustrated 324 Newsweek 312 Cosmopolitan 301 Playboy 301 Via Magazine 275 Southern Living 274 Guideposts 263 American Legion 253 Maxim 250 AAA Going Places 248 Redbook 243 O, the Oprah Magazine 240 Glamour 240 AAA Living 240 Parents 205 Smithsonian 205 U.S. News & World Report 203 Seventeen 203 Money 199 Martha Stewart Living 197 Parenting 193 ESPN the Magazine 189 Real Simple 186 Game Informer 183 Family Fun 180 Men’s Health 178 In Style 177 Entertainment Weekly 176 Country Living 174 Cooking Light 172 Endless Vacation 172 VFW Magazine 169 US Weekly 166 Shape 165 Golf Digest 160 Home & Away 157 1 solutions Answer 350812 by stanbon(57967)   on 2011-11-15 21:20:09 (Show Source): You can put this solution on YOUR website! Please help, I am having so much trouble in this class. construct a frequency distribution with a first class (in ten thousands) of 157–234 next is 235-312 etc. Each class is 77 wide. The highest class must accommodate 761 ---- Then count the number of items that fit in each class. ---- That's the histogram. Cheers, Stan H. ============

Probability-and-statistics/532211: A multiple-choice quiz consists of fifteen questions. Each question has five responses, and only one of the answers is correct. Find the probability of guessing and getting exactly two correct. Round to four decimal places, if necessary. 1 solutions Answer 350811 by stanbon(57967)   on 2011-11-15 21:12:36 (Show Source): You can put this solution on YOUR website! A multiple-choice quiz consists of fifteen questions. Each question has five responses, and only one of the answers is correct. Find the probability of guessing and getting exactly two correct. Round to four decimal places, if necessary. ----------------------- Binomial Problem with n = 15 and p(correct) = 1/5 ----- P(x = 2) = 15C2*(1/5)^2(4/5)^13 = 0.2309 ========================================== Cheers, Stan H. ===============

Probability-and-statistics/532343: Suppose you select a 3-digit number at random from the set of all positive 3-digit numbers. Find each probability. I just don't get this. 1 solutions Answer 350809 by stanbon(57967)   on 2011-11-15 21:07:29 (Show Source): You can put this solution on YOUR website! Suppose you select a 3-digit number at random from the set of all positive 3-digit numbers. Find each probability. I just don't get this. ------------------- 3-digit numbers start at 100 and end with 999 ------- There are 999-100+1 = 900 3-digit numbers. --- Prob of selecting some particular 3-digit number = 1/900 =============================================================== Cheers, Stan H.

Word_Problems_With_Coins/532328: You spend 1/3 of your money then with the change you spend another 1/3 of what is left, then you spend 3/4 of the change and are left with $4.60 how much did you start out with.... 1 solutions Answer 350803 by stanbon(57967)   on 2011-11-15 20:39:40 (Show Source): You can put this solution on YOUR website! You spend 1/3 of your money then with the change you spend another 1/3 of what is left, then you spend 3/4 of the change and are left with $4.60 how much did you start out with.... ---- Let amt you started with be "x". after spending 1/3 you have (2/3)x. after spending 1/3 you have (2/3)^2x after spend ing (3/4) you have (1/4)(2/3)^2x ---- Equation: (1/4)(2/3)^2x = 4.60 --- 0.1111x = 4.60 x = $41.40 ========================= Cheers, Stan H.

Polynomials-and-rational-expressions/532326: write the expression 9n^6+7n^3-6 in quadratic form if possible 1 solutions Answer 350801 by stanbon(57967)   on 2011-11-15 20:35:00 (Show Source): You can put this solution on YOUR website! write the expression 9n^6+7n^3-6 in quadratic form if possible ---- = 9(n^3)^2 + 7n^3 -6 ----------------------------------- Cheers, Stan H. =========

Linear-systems/532313: A basketball player makes a total of 517 shots totaling 1037 points. How many of those shots are 3 point shots and how many are 2 point shots? From the examples in the book, I should have 2 equations: x + y = 517 2x + 3y = 1037 Is this right? How do I begin to solve? 1 solutions Answer 350797 by stanbon(57967)   on 2011-11-15 20:28:41 (Show Source): You can put this solution on YOUR website! x + y = 517 2x + 3y = 1037 ---- Multiply thru 1st equation by 2 to get: 2x + 2y = 2*517 2x + 3y = 1037 ---- Subtract and solve for "y": y = 3 --- Solve for "x": x + y = 517 x + 3 = 517 x = 514 ---- Solution: (514,3) ==================== Cheers, Stan H. ====================

Money_Word_Problems/532306: An investor has a total $18,000 deposited in three different accounts, which earn annual interest of 9%, 7%, and 5%. The account deposited in the 9% account is twice the amount in the 5% account. If the three accounts earn total annual interest of $1340, how much money is deposited in each account? 1 solutions Answer 350791 by stanbon(57967)   on 2011-11-15 20:24:00 (Show Source): You can put this solution on YOUR website! An investor has a total $18,000 deposited in three different accounts, which earn annual interest of 9%, 7%, and 5%. The account deposited in the 9% account is twice the amount in the 5% account. If the three accounts earn total annual interest of $1340, how much money is deposited in each account? ---- Quantity Eq:: n + s + f = 18000 Quantiy Eq: n = 2f Interest Eq: 9n+7s+5f = 134000 ---------------------------------- n + s + f = 18000 n + 0 - 2f = 0 9n +7s + 5f = 134000 ------------------------------- Use any method you know to find: n = 9% investment = $8000 s = 7% investment = $6000 f = 5% investment = $4000 ============================= Cheers, Stan H. =============================