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# Recent problems solved by 'checkley77'

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 Numbers_Word_Problems/314192: 3 times the first of three consecutive numbers is 4 more than 2 times the second. Write an equation and solve the problem.1 solutions Answer 224655 by checkley77(12569)   on 2010-06-14 16:49:34 (Show Source): You can put this solution on YOUR website!X, X+1 & X+2 ARE THE 3 INTEGERS. 3X=2(X+1)+4 3X=2X+2+4 3X-2X=6 X=6 ANS. FOR THE FIRST INTEGER. 6+1=7 ANS. FOR THE SECOND INTEGER. PROOF: 3*6=2*7+4 18=14+4 18=18
 Travel_Word_Problems/314193: Martine leaves home at 9 a.m., bicycling at a rate of 24 mi/hr. Two hours later, John leaves, driving at the rate of 48 mi/hr. At what time will John catch up with Martine?1 solutions Answer 224654 by checkley77(12569)   on 2010-06-14 16:46:23 (Show Source): You can put this solution on YOUR website!D=RT D=24T FOR MARTINE D=48(T-2) FOR JOHN 24T=48(T-2) 24T=48T-96 24T-48T=-96 -24T=-96 T=-96/-24 T=4 HOURS AFTER 9:00 AM THEY WILL MEET.
 Money_Word_Problems/314195: A real estate agent's commission rate is 6%. What will the amount of the commission be on the sale for a 185,000 home?1 solutions Answer 224652 by checkley77(12569)   on 2010-06-14 16:42:14 (Show Source): You can put this solution on YOUR website!Selling price*commissiom percentage=commission value. 185,000*.06=\$11,100 ANS. FOR THE COMMISSION.
 Geometry_Word_Problems/314196: The length of a rectangle is 5 cm less than 3 times its width. If the perimeter of the rectangle is 46 cm, find the dimensions of the rectangle.1 solutions Answer 224651 by checkley77(12569)   on 2010-06-14 16:40:43 (Show Source): You can put this solution on YOUR website!Sorry. I must have bneen tired & misread the problem. You're right. L=3W-5 P=2L+2W 46=2(3W-5)+2W 46=6W-10+2W 46=8W-10 8W=46+10 8W=56 W=56/8 W=7 cm. ANS. FOR THE WIDTH. L=3*7-5=21-5=16 cm. ANS. FOR THE LENGTH. PROOF: 46=2*16+2*7 46=32+14 46=46
 Geometry_Word_Problems/314226: a 5 foot border is added to all four sides of a rectangular playing field of 40 feet by 30 feet.What is the area in square feet of the added border? 1 solutions Answer 224650 by checkley77(12569)   on 2010-06-14 16:34:04 (Show Source): You can put this solution on YOUR website!40*30=1,200 ft^2 is the area of the playing field. (40+10)(30+10)=50*40=2,000 ft^2 is the total area of the field & the border. 2,000-1,200=800ft^2 is the area of the border.
 Money_Word_Problems/314255: Alicia has \$7000 invested; some at 7% and the remainder at 8%. After one year, the interest from the 7% investment exceeds the interest from the 8% investment by \$70. How much is invested at each rate. Thanks in advance for any assistance!1 solutions Answer 224649 by checkley77(12569)   on 2010-06-14 16:30:10 (Show Source): You can put this solution on YOUR website!.08x+70=.07(7,000-x) .08x+70=490-.07x .08x+.07x=490-70 .15x=420 x=420/.15 x=2,800 amount invested @ 8%. 7,000-2,800=4,200 amount invested @ 7%. Proof: .08*2,800+70=.07*4,200 224+70=294 294=294
 Rational-functions/314259: solve: z+9/z= -101 solutions Answer 224647 by checkley77(12569)   on 2010-06-14 16:21:26 (Show Source): You can put this solution on YOUR website!z+9/z= -10 (z*z+9)/z=-10 (z^2+9)/z=-10 cross multiply. z^2+9=-10z z^2+10z+9=0 (z+9)(z+1)=0 z+9=0 z=-9 ans. z+1=0 z=-1 ans.
 Equations/313940: Please help me solve this word problem equation A boat's crew rowed 12 miles downstream, with the current in 2 hours. The return trip upstream against the current covered the same distance but took 3 hours. Find the crew's rowing rate in still water and the rate of the current.1 solutions Answer 224501 by checkley77(12569)   on 2010-06-13 21:24:43 (Show Source): You can put this solution on YOUR website!D=RT 12=R*2 R=12/2 R=6 MPH WITH THE CURRENT. 12=R*3 R=12/3 4 MPH AGAINST THE CURRENT. (6+4)/2=10/2=5 MPH IS THE SPEED OF THE BOAT IN STILL WATER. 6-5=1 MPH FOR THE CURRENT. 5-4=1 DITTO.
 Linear-systems/313987: write an equation of the line containing the given point and parallel to the given line y=mx+b (2,7)x+8y=9 y=1 solutions Answer 224500 by checkley77(12569)   on 2010-06-13 21:12:21 (Show Source): You can put this solution on YOUR website!(2,7) x+8y=9 8y=-x+9 y=-x/8+9/8 (red line) This line has a slope=-1/8. The parallel line will also have a slope=-1/8 7=-1/8*2+b 7=-2/8+b b=7+1/4 b=(28+1)/4 b=29/4 The Y intercept. y=-x/8+29/4 (green line) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -x/8 +9/8 and -x/8 +29/4).
 Problems-with-consecutive-odd-even-integers/313988: The sum of two integers is 10, and their product is 24. Find the two integers.1 solutions Answer 224497 by checkley77(12569)   on 2010-06-13 21:04:58 (Show Source): You can put this solution on YOUR website!x+y=10 or x=10-y xy=24 (10-y)y=24 10y-y^2=24 -y^2+10y-24=0 y^2-10y+24=0 (y-6)(y-4)=0 y-=0 y=6 ans. x=10-6=4 ans. y-4=0 y=4 ans. x=10-4=6 ans. Proof: 4*6=24
 Miscellaneous_Word_Problems/313989: A rectangular pool is 30 feet wide and 40 feet long. It is surrounded on all four sides by a wooden deck that is x feet wide. The total area enclosed within the perimeter of the deck is 3000ft^2. What is the width of the deck?1 solutions Answer 224490 by checkley77(12569)   on 2010-06-13 20:52:39 (Show Source): You can put this solution on YOUR website!(30+2x)(40+2x)=3,000 1,200+80x+60x+4x^2=3,000 4x^2+140x+1,200-3,000=0 4x^2+140x-1800=0 (2x-20)(2x+90)=0 2x-20=0 2x=20 x=20/2 x=10 ft. ans. for the width of the wooden deck. Proof: (30+2*10)(40+2*10)=3,000 (30+20)(40+20)=3,000 50*60= 3,000 3,000=3,000
 Numbers_Word_Problems/313990: You inherit \$10,000 with the stipulation that you for the first year the money must be invested in two stocks paying 6% and 11% annual interest respectively. How much should be invested at each rate if the total interest earned for the the year is to be be \$700?1 solutions Answer 224484 by checkley77(12569)   on 2010-06-13 20:42:27 (Show Source): You can put this solution on YOUR website!.11x+.06(10,000-x)=700 .11x+600-.06x=700 .05x=700-600 .05x=100 x=100/.05 x=2,000 the amount invested @ 11%. 10,000-2,000=8,ooo the amount invested @ 6%. Proof: .11*2,000+.06*8,000=700 220+480700 700=700
 Linear-equations/313991: Write an equation of the line containing the given point and parallel to the given line. (4,-1); 8x-9y=51 solutions Answer 224481 by checkley77(12569)   on 2010-06-13 20:37:00 (Show Source): You can put this solution on YOUR website!(4,-1); 8x-9y=5 -9y=-8x+5 y=-8x/-9+5/-9 y=8x/9-5/9 This line has a slope=8/9. (red line) The parallel line will also have a slope=8/9. -1=8/9*5+b -1=40/9+b b=-1-40/9 b=-9/9-40/9 b=-49/9 the Y intercept. y=8x/9-49/9 is the equation for the parallel line. (green line). (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 8x/9 -5/9 and 8x/9 -49/9).
 Rate-of-work-word-problems/313993: A mason can build a wall in 10 hours. An apprentice can build a wall in 15 hours. How long would it take them to build the wall if they worked together?1 solutions Answer 224479 by checkley77(12569)   on 2010-06-13 20:29:20 (Show Source): You can put this solution on YOUR website!1/10+1/15=1/x (15+10)/10*15=1/x 25/150=1/x 1/6=1/x x=6 hours ans. when they work together,
 Linear-equations/313994: y=-6/5+41 solutions Answer 224477 by checkley77(12569)   on 2010-06-13 20:26:02 (Show Source): You can put this solution on YOUR website!y=-6/5+4 y=-6/5+20/5 y=(-6+20)/5 y=14/5 ans.
 Graphs/314002: could you help me solve 2x-y=1 8x-4y=-8 by graphing1 solutions Answer 224475 by checkley77(12569)   on 2010-06-13 20:23:04 (Show Source): You can put this solution on YOUR website!2x-y=1 -Y=-2X+1 Y=2X-1 (RED LINE) 8x-4y=-8 -4Y=-8X-8 4Y=8X+8 Y=8X/4+8/4 Y=2X+2 (GREEN LINE) (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions 2x =1 and 2x +2). These two lines are parallel thus no intersection & no unique solution.
 Travel_Word_Problems/314004: Two cars leave philadelphia, one traveling north and the other traveling south. After 3 hours, they are 297 miles apart. If one car is traveling 5 miles per hour faster than the other, what is the speed of each?1 solutions Answer 224473 by checkley77(12569)   on 2010-06-13 20:16:58 (Show Source): You can put this solution on YOUR website!D=RT 297=(X+X+5)3 297=(2X+5)3 297=6X+15 6X=297-15 6X=282 X=282/6 X=47 MPH. FOR THE SLOWER CAR. 47+5=52 MPH. FOR THE FASTER CAR. PROOF: 297=(47+52)3 297=99*3 297=297
 Problems-with-consecutive-odd-even-integers/313933: The product of two positive consecutive integers is 41 more than their sum. Find the integers1 solutions Answer 224470 by checkley77(12569)   on 2010-06-13 20:08:58 (Show Source): You can put this solution on YOUR website!X(X+1)=X+X+1+41 X^2+X=2X+42 X^2+X-2X-42=0 X^2-X-42=0 (X-7)(X+6) X-7=0 X=7 ANS. X+6=0 X=-6 ANS. PROOF: 7(7+1)=7+8+41 7*8=15+41 56=56 -6(-5)=-6-5+41 30=-11+41 30=30
 Equations/313942: Please help me solve this word problem equation, A store mixes Kenyan coffee worth \$10 per kilogram and Turkish coffee worth \$12 per kilogram.The mixture is to sell for \$11 per kilogram.Find how much of each should be used to make a 588-kilogram mixture. How many kilograms of the Kenyan coffee should be in the mixture? How many kilograms of the Turkish coffee should be in the mixture?1 solutions Answer 224468 by checkley77(12569)   on 2010-06-13 20:00:19 (Show Source): You can put this solution on YOUR website!12X+10(588-X)=588*11 12X+5,880-10X=6,468 2X=6,468-5,880 2X=588 X=588/2 X=294 POUNDS OF \$12 COFFEE IS USED. 588-294=294 LOUNDS OF \$10 COFFEE IS USED. PROOF: 12*294+10*294=588*11 3,528+2,940=6,468 6,468=6,468
 Numbers_Word_Problems/313954: The sum of two numbers is 2. Five times the first number equals 2 times the second number. Find the two numbers1 solutions Answer 224467 by checkley77(12569)   on 2010-06-13 19:53:53 (Show Source): You can put this solution on YOUR website!X+Y=2 OR X=2-Y 5X=2Y 5(2-Y)=2Y 10-5Y=2Y -5Y-2Y=-10 -7Y=-10 Y=-10/-7 Y=10/7 ANS. X=2-10/7 Y=14/7-10/7 X=4/7 ANS. PROOF: 5*4/7=2*10/7 20/7=20/7
 Numbers_Word_Problems/313958: Jimmy is a partner in an Internet-based coffee supplier.The company offers gourmet coffee beans for \$13 per pound and regular coffee beans for \$4 per pound. Jimmy is creating a product that will sell for \$6 per pound.The first thing to go into the mixing bin was 18 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?1 solutions Answer 224466 by checkley77(12569)   on 2010-06-13 19:49:39 (Show Source): You can put this solution on YOUR website!18*13+4X=6(18+X) 234+4X=108+6X 4X-6X=108-234 -2X=-126 X=-126/-2 X=63 POUNDS OF \$4 COFFEE IS USED. PROOF: 18*13+4*63=6(18+63) 234+252=6*81 486=486
 Numbers_Word_Problems/313961: The length of a rectangular room is 6 feet longer than twice the width.If the room's perimeter is 144 feet, what are the room's dimension's?1 solutions Answer 224465 by checkley77(12569)   on 2010-06-13 19:44:24 (Show Source): You can put this solution on YOUR website!L=2W+6 P=2L+2W 144=2(2W+6)+2W 144=4W+12+2W 144=6W+12 6W=144-12 6W=132 W=132/6 W=22 FT. ANS. FOR THE WIDTH. L=2*22+6 L=44+6=50 FT. ANS. FOR THE LENGTH. PROOF: 144=2*50+2*22 144=100+44 144=144
 Quadratic_Equations/313962: find the roots of 4x^2=3x+2 to the nearest hundreth.1 solutions Answer 224464 by checkley77(12569)   on 2010-06-13 19:40:41 (Show Source): You can put this solution on YOUR website!4x^2=3x+2 4x^2-3x-2=0 x=(3+-sqrt[-3^2-4*4*-2])/2*4 x=(3+-sqrt[9+36])/8 x=(3+-sqrt41)/68x=(3+-6.403)/6 x=(3+6.403)/8 x=9.403/8 x=1.175 ans. x=(3-6.403)/8 x=-3.403/8 x=-.425 ans.
 Linear-equations/313966: write the equation of the line parallel to the equation y=-1/4x+7 and passes through the ordered pair (0,15)1 solutions Answer 224463 by checkley77(12569)   on 2010-06-13 19:33:12 (Show Source): You can put this solution on YOUR website!y=-1/4x+7 (red line) and passes through the ordered pair (0,15). THIS LINE HAS A SLOPE=-1/4. THE PARALLEL LINE WILL ALSO HAVE A SLOPE=-1/4 15=-1/4*0+b 15=b the Y intercept of the parallel line. Y=-x/4+15 (green line)is the equation for the parallel line passing through (0,15). (graph 300x200 pixels, x from -6 to 15, y from -10 to 20, of TWO functions -x/4 +7 and -x/4 +15).
 Quadratic_Equations/313972: a man invested a total of \$15000 in two venture..in one he made profit of 8% and in other 4% loss..his net income from the two venture is 240\$..how much did he invested in each venture?1 solutions Answer 224462 by checkley77(12569)   on 2010-06-13 19:26:08 (Show Source): You can put this solution on YOUR website!.08X-.04(15,000-X)=240 .08X-600+.04X=240 .12X=240+600 .12X=840 X=840/.12 X=%7,000 INVESTED @ 8%. 12,000=7,000=\$8,000 INVESTED @ 4%. PROOF: .08*7,000-.04(8,000)=240 560-320=240 240=240
 Finance/313974: An investment has grown to \$89,000 over a 6-year period. The interest was computed daily and the rate was 7 3/8 % per year. What was the original investment? 1 solutions Answer 224461 by checkley77(12569)   on 2010-06-13 19:19:33 (Show Source): You can put this solution on YOUR website!X(1+.07375/365)^6*365=89,000 X(1+.000202)^2,190=89,000 X(1.000202)^2,190=89,000 X*1.556=89,000 X=89,000/1.556 X=\$57,197.94 WAS THE ORIGINAL INVESTMENT.
 Surface-area/313979: the area of a rectangle is 216 cm2. the base is three more than three times the height. What is the perimeter?1 solutions Answer 224460 by checkley77(12569)   on 2010-06-13 19:12:15 (Show Source): You can put this solution on YOUR website!B=3H+3 A=BH 216=(3H+3)H 216=3H^2+3H 3H^2+3H-216=0 3(H^2+H-72)=0 3(H+9)(X-8)=0 H-8=0 H=8 ANS. FOR THE HEIGHT. B=3*8+3 B=24+3=27 ANS. FOR THE BASE. PROOF: 216=8*27 216=216
 logarithm/313980: All i know is the question, 1+ the square root of (x+5) this is equal to the square root of (x+12) Now what is x?? 1 solutions Answer 224459 by checkley77(12569)   on 2010-06-13 19:06:36 (Show Source): You can put this solution on YOUR website!1+sqrt(x+5)=sqrt(x+12) square botgh sides. 1+2sqrt(x+5)+x+5=x+12 x-x+2sqrt(x+5)=12-5-1 2sqrt(x+5)=6 square both sides. 4(x+5)=36 4x+20=36 4x=36-20 4x=16 x=16/4 x=4 ans. Proof: 1+sqrt(4+5)=sqrt(4+12) 1+sqrt9=sqrt16 1+3=4 4=4
 Linear-systems/313981: find the slope and y intercept of the line 3y+3x+2=11+3x1 solutions Answer 224458 by checkley77(12569)   on 2010-06-13 18:57:01 (Show Source): You can put this solution on YOUR website!3y+3x+2=11+3x 3Y=3X-3X+11-2 3Y=9 Y=9/3 Y=3 THE Y INTERCEPT=3. SLOPE IS=0. (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = 3).
 Geometry_Word_Problems/313917: A spherical storage tank has a diameter of 48 ft and is full of water. How many delivery trucks with cylindrical tanks measuring 8 ft in diameter and 10 ft long can be completely filled from the storage tank? A) 230 trucks B) 115 trucks C) 86 trucks D) 1152 trucks 1 solutions Answer 224455 by checkley77(12569)   on 2010-06-13 18:50:50 (Show Source): You can put this solution on YOUR website!V=4/3PI*R^3 V=4/3*3.14*24^3 V=4.187*13,824 V=57,881.09 TANK VOLUME. V=PI*R^2*H V=3.14*4^2*10 V=3.14*16^10 V=3.14*160 V=502.4 VOLUME OF THE TANKER TRUCK. 57,881.09/502.4=115.21 TANKER TRUCK LOADS ARE REQUIRED TO EMPTY THE TANK. ANSWER B)
 Travel_Word_Problems/313919: Two bicyclists start at the same time at a given point and travel in the same direction at average speeds of 8 miles per hour and 10 miles per hour. After how long are the bicyclists 5 miles apart?1 solutions Answer 224451 by checkley77(12569)   on 2010-06-13 18:39:06 (Show Source): You can put this solution on YOUR website!D=RT D=8T D=10T-5 8T=10T-5 8T-10T=-5 -2T=-5 T=-5/-2 T=2/5 T=2.5 HOURS THEY WILL BE 5 MILES APART. PROOF: 8*2.5=10*2.5-5 20=25-5 20=20