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# Recent problems solved by 'checkley77'

checkley77 answered: 12560 problems
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 Quadratic_Equations/264597: 2a-5b=4 5a-2b=31 solutions Answer 194773 by checkley77(12569)   on 2010-02-02 16:25:06 (Show Source): You can put this solution on YOUR website!2a-5b=4 multiply by 5 5a-2b=3 multiply by -2 & add. 10a-25b=20 -10a+4b=-6 ------------- -21b=14 b=14/-21 b=-2/3 ans. 2a-5*-2/3=4 2a+10/3=4 2a=4-10/3 2a=(4*3-10)/3 2a=(12-10)/3 2a=2/3 a=(2/3)/2 a=2/3*1/2 a=2/6=1/3 ans. Proof: 5*1/3-2*-2/3=3 5/3+4/3=3 9/3=3 3=3
 Finance/264258: A man purchased a number of books at \$7.00 and twice as many books at \$12.50 each. The total cost came to \$768. If x is the number of \$7.00 books purchases, write down an equation and solve it to find the number of books purchased.(round your answer to the nearest book) I am getting confused by the missing total amount of books. It is supposedly 3x to get the thirds, but there I can't get the answer. 1 solutions Answer 194590 by checkley77(12569)   on 2010-02-01 21:32:44 (Show Source): You can put this solution on YOUR website!7x+12.50*2x=768 7x+25x=768 32x=768 x=768/32 x=24 \$7 books were purchased. 2*24=48 \$12.50 books were purchased. Proof: 7*24+48*12.50=768 168+600=768 768=768
 Money_Word_Problems/264262: A woman got a job at a starting salary of \$35,000 a year. If she received am 8% raise on each additional year, how much would her salary be at the beginning of the tenth year? (use future value method) 1 solutions Answer 194585 by checkley77(12569)   on 2010-02-01 21:27:29 (Show Source): You can put this solution on YOUR website!35,000(1+.08)^10 35,000*1.08^10 35,000*2.1589=\$75,562.37 ans. for the salary in the tenth year.
 Linear_Equations_And_Systems_Word_Problems/264270: A financial planner wants to invest \$8000, some in stock earning 15% annually and the rest in bonds earning 6% annually. How much should be invested at each rate to get a return of \$930 annually from the two investments?1 solutions Answer 194582 by checkley77(12569)   on 2010-02-01 21:23:32 (Show Source): You can put this solution on YOUR website!.15x+.06(8,000-x)=930 .15x+480-.06x=930 .09x=930-480 .09x=450 x=450/.09 x=5,000 invested @ 15%. 8,000-5,000=3,000 invested @ 6% Proof: .15*5,000+.06*3,000=930 750+180=930 930=930
 Permutations/264271: how many different ways can a president, cie president, and secretary be chosen from a class of 15 students1 solutions Answer 194578 by checkley77(12569)   on 2010-02-01 21:20:08 (Show Source): You can put this solution on YOUR website!nPr where n=15 & r=3 n!/r!(n-r)! 15!/3!(15-3)! 15!/3!12!=2,730 possible choices.
 Equations/264272: 4n+5=6n+71 solutions Answer 194575 by checkley77(12569)   on 2010-02-01 21:01:35 (Show Source): You can put this solution on YOUR website!4n+5=6n+7 4n-6n=7-5 -2n=2 n=2/-2 n=-1 Proof: 4*-1+5=6*-1+7 -4+5=-6+7 1=1
 Linear-systems/264208: x + 14y= 84 2x - 7y = -7 how do i solve these equations using substation? 1 solutions Answer 194572 by checkley77(12569)   on 2010-02-01 20:57:35 (Show Source): You can put this solution on YOUR website!x + 14y= 84 x=84-14y substitute (84-14y) for x in the other equation & solve for y. 2x - 7y = -7 2(84-14)-7y=-7 168-28y-7y=-7 -35y=-7-168 -35y=-175 y=-175/-35 y=5 ans. x=84-14*5 x=84-70 x=14 ans. Proof: 2*14-7*5=-7 28-35=-7 -7=-7
 Linear_Equations_And_Systems_Word_Problems/264209: I need to find the y-intercept of: 2x divided by 3y= -12 Thank you for your help!1 solutions Answer 194567 by checkley77(12569)   on 2010-02-01 20:51:40 (Show Source): You can put this solution on YOUR website!Y=mX+b b=the y intercept. 2x divided by 3y= -12 2x/3y=-12 cross multiply. 3y*-12=2x -36y=2x divide by -36 y=-2x/-36 Y=X/18 [For this line equation the y intercept=0] (graph 300x200 pixels, x from -16 to 15, y from -10 to 10, y = x/18).
 Linear-systems/264210: 3x - 2y = 11 x - y/2 = 4 how do i solve these equations using substation? 1 solutions Answer 194565 by checkley77(12569)   on 2010-02-01 20:44:54 (Show Source): You can put this solution on YOUR website!3x - 2y = 11 x - y/2 = 4 multiply by 3 & subtract. 3x-2y=11 -(3x-3y/2=12) ---------------- -2y+3y/2=-1 (-2y*2+3y)/2=-1 (-4y+3y)/2=-1 -y/2=-1 -y=-2 y=2 ans. 3x-2*2=11 3x-4=11 3x=11+4 3x=15 x=15/3 x=5 Proof: 5-2/2=4 5-1=4 4=4
 Mixture_Word_Problems/264211: Anna worked two part-time jobs last week. The first job paid \$11 an hour, and the second job paid \$14 an hour. She worked a total of 26 hours last week and earned \$319. How many hours did Anna work at the first job? Write an equation you can use to answer this question. Let x be the number of hours worked at the first job. Use your equation to solve the problem. 1 solutions Answer 194561 by checkley77(12569)   on 2010-02-01 20:35:59 (Show Source): You can put this solution on YOUR website!11x+14(26-x)=319 11x+364-14x=319 -3x=319-364 -3x=-45 x=-45/-3 x=15 hours were worked @ the first job. 26-15=11 hours were worked @ the second job. Proof: 11*15+14*11=319 165+154=319 319=319
 Surface-area/264220: What is width of a rectangle if the length is 5 in. and the area is 30 square in.? 1 solutions Answer 194560 by checkley77(12569)   on 2010-02-01 20:31:40 (Show Source): You can put this solution on YOUR website!LW=30 5W=30 W=30/5 W=6 in. answer for the width.
 Volume/264224: Solve the problem. An open box is to be made from a square piece of sheet metal by removing a square of side 3 inches from each corner and turning up the edges. If the volume of the box is to be 1728 cubic inches, what is the length of the sides of the square of the sheet metal.1 solutions Answer 194559 by checkley77(12569)   on 2010-02-01 20:28:26 (Show Source): You can put this solution on YOUR website!3(x-2*3)^2=1728 3(x-6)^2=1728 3(x^2-12x+36=1728 3x^2-36x+108-1728=0 3x^2-36x-1620=0 3(x^2-12x-540)=0 3(x-30)(x+18)=0 x-30=0 x=30 30-2*3 30-6-24 is the sides of the square base. Proof: 3*24^2=1728 3*576=1728 1728=1728
 decimal-numbers/264226: express the decimal number 4693 as a binary number1 solutions Answer 194554 by checkley77(12569)   on 2010-02-01 20:18:28 (Show Source): You can put this solution on YOUR website!4,693=1001001010101 Proof: 4096*1=4096 2048*0=0 1024*0=0 512*1=512 256*0=0 128*0=0 64*1=64 32*0=0 16*1=16 8*0=0 4*1=4 2*0=0 1*1=1 ---------- 4,693
 Equations/264164: Six hundred people attended the premiere of a motion picture. Adult tickets cost \$7, and children were admitted for \$2. If box office receipts totaled \$3950, how many children attended the premiere?1 solutions Answer 194543 by checkley77(12569)   on 2010-02-01 19:59:09 (Show Source): You can put this solution on YOUR website!A+C=600 or C=600-A 7A+2C=3,950 7A+2(600-A)=3,950 7A+1,200-2A=3,950 5A=3,950-1,200 5A=2,750 A=2,750/5 A=550 ADULT TICKETS WERE SOLD. 600-550=50 CHILDREN'S TICKETS WERE SOLD. PROOF: 7*550+2*50=3,950 3,850+100=3,950 3,950=3,950
 Signed-numbers/264166: 8= -64y I don't understand how or why to get y1 solutions Answer 194542 by checkley77(12569)   on 2010-02-01 19:54:39 (Show Source): You can put this solution on YOUR website!8= -64y divide both sides by -64 8/-64=-64y/-64 -1/8=y ans. Proof: 8=-64*-1/8 8=64/8 8=8
 Systems-of-equations/264174: what is 6x-2y=10 x-2y=-5?1 solutions Answer 194541 by checkley77(12569)   on 2010-02-01 19:51:29 (Show Source): You can put this solution on YOUR website!6x-2y=10 -(x-2y=-5) subtract. ------------------ 5x=15 x=15/5 x=3 ans. 3-2y=-5 -2y=-5-3 -2y=-8 y=-8/-2 y=4 ans. Proof: 6*3-2*4=10 18-8=10 10=10
 Quadratic-relations-and-conic-sections/264185: w^2-4=3w1 solutions Answer 194538 by checkley77(12569)   on 2010-02-01 19:43:18 (Show Source): You can put this solution on YOUR website!w^2-4=3w w^2-3w-4=0 (w-4)(w+1)=0 w-4=0 w=4 ans. w+1=0 w=-1 ans.
 Expressions-with-variables/264187: how do you do substitution. like y=2x+7 and 3x-y=-9. if you could help plz1 solutions Answer 194536 by checkley77(12569)   on 2010-02-01 19:40:36 (Show Source): You can put this solution on YOUR website!y=2x+7 replace y with (2x+7) in the second equation & solve for x. 3x-y=-9 3x-(2x+7)=-9 3x-2x-7=-9 x=-9+7 x=-2 ans. y=2*-2+7 y=-4+7 y=3 ans. Proof: 3*-2-3=-9 -6-3=9 -9=-9
 Linear-equations/264154: Could you please help me get started with this problem? Recycled 38 in 1990, 45 in 1991, 45 in 1992, 47 in 1994, 60 in 2001. slope intercept form is y=2.1x+37. y=recycled numbers x= year number coded as 1990=1, 1992=3, 1994=5, 2001=12. Is slope negative or postive? Calculate x-intercept year, what is it and what is the meaning of this point for the data? If you could help me get started I would really appreciate it. I have gotten totally confused. Thank you1 solutions Answer 194534 by checkley77(12569)   on 2010-02-01 19:33:58 (Show Source): You can put this solution on YOUR website!Y=mX+b m=slope m=2.1 which is positive. y=2.1x+37 (graph 300x200 pixels, x from -206 to 5, y from -10 to 50, 2.1x +37). 0=2.1x+37 2.1x=-37 x=-37/2.1 x=17.619 ans for the x intercept. 1990-18=1972 is the year there was no recycling.
 Complex_Numbers/264155: 81x^2 -4y^2 divided by 9x^2 - 25xy - 6y^21 solutions Answer 194528 by checkley77(12569)   on 2010-02-01 19:18:35 (Show Source): You can put this solution on YOUR website!(81x^2 -4y^2)/(9x^2 - 25xy - 6y^2) factor both numerator & denominator. (9x+2y)(9x-2y)/(9x+2y)(x-3y) cancel the common terms (9x+2y. (8x-2y)/(x-3y) ans.
 Miscellaneous_Word_Problems/264156: From a survey of 600 college students, a marketing research company found that 400 students owned stereos, 200 owned cars, and 75 owned both cars and stereos. (a) How many students owned either a car or a stereo (but not both)? (b) How many students do not own either a car or a stereo? 1 solutions Answer 194524 by checkley77(12569)   on 2010-02-01 19:14:52 (Show Source): You can put this solution on YOUR website!(400+200)-75=600-75=525 students owned a car or a stereo but not both. 600-525=75 students did not own either a car or a stereo.
 Numeric_Fractions/264157: 4/m / 5m/91 solutions Answer 194522 by checkley77(12569)   on 2010-02-01 19:08:33 (Show Source): You can put this solution on YOUR website!4/m / 5m/9 Invert the denominator & multiply. 4/m*9/5m multiply numerators & denominators. 4*9=36 is the numerator. m*5m=5*m*m=5m^2 is the denominator. 36/5m^2 ans.
 Graphs/264116: Solve each system by graphing 4x-y=9 2x+3y=27. (0,-9) 1 solutions Answer 194521 by checkley77(12569)   on 2010-02-01 19:05:22 (Show Source): You can put this solution on YOUR website!4x-y=9 -y=-4x=9 y=4x-9( red line) 2x+3y=27 3y=-2x+27 y=-2x/3+27/3 y=-2x/3+9 (green line) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 4x -9 and -2x/3 +9). Intercept=(4,7) (0,-9)
 Linear_Equations_And_Systems_Word_Problems/264127: A 17-foot piece of string is cut into two pieces so that the longer piece is 2 feet longer than twice the shorter piece. Find the lengths of both pieces.1 solutions Answer 194519 by checkley77(12569)   on 2010-02-01 18:58:46 (Show Source): You can put this solution on YOUR website!x+2x+2=17 3x=17-2 3x=15 x=15/3 x=5 ft. for the short piece. 17-5=12 ft. for the longer piece. Proof: 5+2*5+2=17 5+10+2=17 17=17
 Mixture_Word_Problems/264128: exam has 40 questions and is worth 10%. how much is each question worth?1 solutions Answer 194517 by checkley77(12569)   on 2010-02-01 18:56:02 (Show Source): You can put this solution on YOUR website!.10/40=.0025 or .25% for each question.
 Geometry_Word_Problems/264129: a rectangular field is 900 yards by 240 yards. What is the greatest number of rectangular lots of 120 yards by 60 yards that it can be divided into?1 solutions Answer 194515 by checkley77(12569)   on 2010-02-01 18:53:53 (Show Source): You can put this solution on YOUR website!900*240/120*60 216,000/7,200=30 lots are possible. Proof: 900/60*240/120=15*2=30
 Quadratic-relations-and-conic-sections/264130: How do you do ; 5m^2+40m+75=0?1 solutions Answer 194513 by checkley77(12569)   on 2010-02-01 18:49:52 (Show Source): You can put this solution on YOUR website!5m^2+40m+75=0 5(m^2+8m+15)=0 5(m+5)(m+3)=0 m+5=0 m=-5 ans. m+3=0 m=-3 ans.
 Polynomials-and-rational-expressions/264131: 144a^2 - 49b^21 solutions Answer 194511 by checkley77(12569)   on 2010-02-01 18:47:34 (Show Source): You can put this solution on YOUR website!144a^2 - 49b^2 (12A+7B)(12A-7B) ans.
 Mixture_Word_Problems/264132: A total of \$20,000 is invested in two bonds that pay 8% and 9.5% simple intrest. The annual intrest is \$1675. How much is interested in each bond?1 solutions Answer 194510 by checkley77(12569)   on 2010-02-01 18:46:29 (Show Source): You can put this solution on YOUR website!.095X+.08(20,000-X)=1,675 .095X+1,600-.08X=1,675 .015X=1,675-1,600 .015X=75 X=75/.015 X=5,000 INVESTED @ 9.5% 20,000-5,000=15,000 INVESTED @ 8% PROOF: .095*5,000+.08*15,000=1,675 475+1,200=1,675 1,675=1,675
 Problems-with-consecutive-odd-even-integers/264140: find three consecutive integers such that the sum of twice the first and 4 times the second is equal to 20 more than twice the third1 solutions Answer 194507 by checkley77(12569)   on 2010-02-01 18:42:11 (Show Source): You can put this solution on YOUR website!LET X, X+1 & X+2 BE THE 3 INTEGERS. 2X+4(X+1)=2(X+2)+20 2X+4X+4=2X+4+20 2X+4X-2X=24-4 4X=20 X=20/4 X=5 ANS. FOR THE FIRST INTEGER. 5+1=6 FOR THE NEXT INTEGER. 5+2=7 FOR THE LARGEST INTEGER. PROOF: 2*5+4*6=2*7+20 10+24=14+20 34=34
 Proportions/264134: I have one question, Miracle wants to sell a 40 fluid oz bottle at the same unit rate of the 12 fluid oz bottle (hint: The 12 fluid oz is \$1.32 a bottle) how much will she charge for the 40 fluid oz? 1 solutions Answer 194504 by checkley77(12569)   on 2010-02-01 18:36:54 (Show Source): You can put this solution on YOUR website!12/40=1.32/X CROSS MULTIPLY 12X=40*1.32 12X=52.8 X=52.8/12 X=\$4.40 SHOULD BE THE PRICE OF THE 40 OZ. BOTTLE. PROOF: 12/40=1.32/4.40 12*4.40=40*1.32 52.8=52.8