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# Recent problems solved by 'ptaylor'

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 Word_Problems_With_Coins/501638: a man has two more dimes than quarters and three times as many nicles as dinmes, Altogether he has 2.50. How many of each coin does he have1 solutions Answer 338599 by ptaylor(2048)   on 2011-09-21 05:27:48 (Show Source): You can put this solution on YOUR website!Let x=number of quarters Then x+2=number of dimes And 3(x+2)=number of nickels Now lets deal in pennies: 25x+10(x+2)+3*5(x+2)=250 25x+10x+20+15x+30=250 subtract 20 and 30 from each side 25x+10x+20-20+15x+30-30=250-20-30 collect like terms 50x=200 x=4-------------------------number of quarters x+2=4+2=6----------------------number of dimes 3(x+2)=3*6=18-------------------number of nickels CK 4*25=100 6*10=60 18*5=90 100+60+90=250 250=250 Hope this helps----ptaylor
 Linear-systems/501062: How do i classify the linear system stated here : {x+4=y {5y=5x+35 Can you help me by telling me what to do? I get lost .. I figured it out until the point of : 5y=(-5x-20)+35 ? I don't know the next step .. Help would be much appreciated .. Thanks :)1 solutions Answer 338422 by ptaylor(2048)   on 2011-09-20 15:40:50 (Show Source): You can put this solution on YOUR website!OK x+4=y subtract 4 and also y from each side x-y=-4----------------------eq1 5y=5x+35 subtract 5y and also 35 from each side 5x-5y=-35 divide each term by 5 x-y=-5-----------------------eq 2 Equations 1 and 2 represent parallel lines, therefore they are independent and inconsistent Hope this helps---ptaylor
 Travel_Word_Problems/501107: You drive 20 miles at 55 mph, then 5 miles at 40 mph and finally, 2 miles at 25 mph. What is your average speed for this trip?1 solutions Answer 338416 by ptaylor(2048)   on 2011-09-20 15:27:59 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r also Average speed =(total distance)/(total time) Total distance=20+5+2=27 miles Time traveling at 55 mph=20/55=4/11 hr Time travelling at 40 mph=5/40=1/8 hr Time traveling at 25 mph=2/25 hr Total time=4/11 +1/8 + 2/25=0.364 +0.125+0.08=0.569 hr Average speed=27/0.569=47.452 mph Hope this helps----ptaylor
 Rate-of-work-word-problems/498803: The erection of a tower takes 24 men to complete in 15 days. How many days will it take 9 men to erect if they work at the same rate?1 solutions Answer 337178 by ptaylor(2048)   on 2011-09-16 05:45:58 (Show Source): You can put this solution on YOUR website!If 24 men can complete the tower in 15 days, there are 24*15=360 man-days of labor involved in the project In other words, 1 man can complete the project in 360 days. 9 men can complete the job in 360/9=40 days And, of course, it takes 24 men 360/24=15 days to complete the job Another way: Let x=number of days it takes 9 men to do the job The men work at the rate of 1/360 of the project per day so, (9/360)*x=1 (1 tower, that is) 9x=360 x=40 days Hope this helps---ptaylor
 Mixture_Word_Problems/498748: If have a 50 lb. bag of dry powder that is to be mixed with 6.5 quarts of water, but I only need to mix a very small amount of the product. If I want to use only 1/2 lb. of powder, how much water would I use? 1 solutions Answer 337177 by ptaylor(2048)   on 2011-09-16 05:23:37 (Show Source): You can put this solution on YOUR website!Let x=amount of water needed Now we can set up a simple ratio: 50 is to 6.5 as 0.5 is to x and we write this as follows: 50/6.5=0.5/x multiply each term by 6.5x (or simply cross-multiply) 50x=3.25 x= 0.065 qts per 1/2lb----amount of water needed CK (100)*(1/2)gal=50gal 100*0.065=6.5 qts Hope this helps---ptaylor
 Travel_Word_Problems/498797: you are driving 65mi/h and take your eyes of the road for just a second. what distance in feet do you travel in this time ? 1 solutions Answer 337176 by ptaylor(2048)   on 2011-09-16 05:04:47 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r Let change mi/hr into ft/sec: 1mi=5280ft 1 hr=60*60=3600sec, soooo 1 mi/hr=5280ft/3600sec=1.467 ft/sec, soooo 65 mi/hr=65*(1.467) ft/sec=95 1/3 ft Hope this helps---ptaylor
 Miscellaneous_Word_Problems/498718: Leslie set up a fruit stand to sell some of her crop of oranges. The first person who came by brought 1/3 of her oranges. The second person brought 4. The third person brought 1/4 of the remaining oranges. Leslie took the last 15 oranges home and made orange juice. How many oranges did leslie have at the beginning?1 solutions Answer 337175 by ptaylor(2048)   on 2011-09-16 04:52:38 (Show Source): You can put this solution on YOUR website!Let x=number of oranges that Leslie had at the beginning After the first person came and bought a third, she had x-(1/3)x=(2/3)x left After the second person bought 4, she had (2/3)x-4 left After the third person bought a fourth of the remaining, she had ((2/3)x-4))-1/4((2/3)x-4) left and we are told this equals 15, sooooo ((2/3)x-4)-1/4((2/3)x-4)=15 lets first multiply each term by 4 4(2/3)x-4)-(2/3)x+4=60 (8/3)x-16-(2/3)x+4=60 (6/3)x-12=60 2x=72 x=36----amount she had at the beginning Ck 36-(1/3)*36=24 24-4=20 20-(1/4)*20=15 15=15 Hope this helps---ptaylor
 Age_Word_Problems/498187: Two years ago, a man was eight times as old as his son. In three years time, he will be four and a half times his son's age then. Find their present ages.1 solutions Answer 336936 by ptaylor(2048)   on 2011-09-15 05:46:59 (Show Source): You can put this solution on YOUR website!Let x=son's present age And let y father's present age x-2=son's age 2 yrs ago; x+3=son's age 3 yrs hence y-2=fathers age 2 yrs ago; y+3=father's age 3 yrs hence Now we are told the following: y-2=8(x-2) simplify y-2=8x-16 y-8x=-14-------------------eq1 and y+3=4.5(x+3)simplify y+3=4.5x+13.5 y-4.5x=10.5----------------eq2 subtract eq1 from eq2 3.5x=24.5 x=7 yrs old-----------------present age of son from eq1 y-56=-14 y=42---------------present age of father CK two years ago: 42-2=8*5 40=40 3 years from present: 42+3=(4.5)*10 45=45 Hope this helps-----ptaylor
 Travel_Word_Problems/497457: A train is traveling at 55mph. A man pitches a baseball at 55mph off the front of the train. What is the speed of the ball? 1 solutions Answer 336735 by ptaylor(2048)   on 2011-09-14 05:26:53 (Show Source): You can put this solution on YOUR website!Initial speed of ball=55mph---------------------speed of train Final speed of ball=initial speed(55mph) + speed that it was pitched(55mph)=110mph for a brief period until it slows down. Try dropping something eco-friendly out the window of a moving car and observe what it does. It will head out in the direction the car is traveling, bouncing along the highway, at the same speed of the car for a brief instance. Hope this helps-----ptaylor
 Travel_Word_Problems/495923: two cars leave from the same location and go in opposite directions. The north bound car travels 15mph slower than the south bound car. After 6 hours they are 630 miles apart. Find the rate of each car. How would i set this equation up to find the value of (X) if (X) is the rate of the cars1 solutions Answer 336265 by ptaylor(2048)   on 2011-09-12 05:05:19 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r Now you need to think about this a little. The cars are traveling at different rates, so X can't be the "rate of the cars". But X can be the rate of one of the cars: Let X=rate of north-bound car Then X+15=rate of south-bound car Distance north-bound car travels after 6 hours=X*6 Distance south-bound car travels after 6 hours=(x+15)*6 Now we are told that these two distances add up to 630 mi, soooo 6X+6(X+15)=630 get rid of parens 6X+6X+90=630 subtract 90 from each side 12X=540 X=45 mph---------------------------rate of north-bound car X+15=45+15=60 mph----------------------rate of south-bound car CK 45*6+60*6=630 270+360=630 630=630 Another way: We know the cars are separating at the rate of X+X+15mph=2X+15 mph in 6 hours they have traveled (2X+15)*6=12X+90 miles and we are told that this equals 630 mi, sooo 12X+90=630----same as before Hope this helps---ptaylor
 Polynomials-and-rational-expressions/495929: please help with method of solution for n/2-1/3=13/61 solutions Answer 336262 by ptaylor(2048)   on 2011-09-12 04:48:38 (Show Source): You can put this solution on YOUR website!(n/2)-1/3=13/6 First, lets get rid of the fractions. We do this by multiplying each term in the equation by the lowest common denominator which is 6, sooo 6*(n/2)-6*(1/3)=6*(13/6) and this gives us 3n-2=13 add 2 to each side 3n-2+2=13+2 collect like terms 3n=15 divide each side by 3 n=5 CK (5/2)-1/3=13/6 we could multiply by the lowest common denominator again or we could just add the fractions. Lets add the fractions: 5/2=15/6 (multiply numerator and denominator by 3) 1/3=2/6 (multiply numerator and denominator by 2), sooooo 15/6-2/6=13/6 13/6=13/6 Note that I used parens for some of the fractions (eg (n/2)) just to make sure there is no confusion. n/2-1/3 could be read as n/(2-1/3) or (n/2)-1/3 Parens helps to underscore that some expressions are one quantity. Hope this helps----ptaylor
 Mixture_Word_Problems/495605: A pot contains 2 L of brine at a concentration of 90 g/L. How much of the water should be boiled off to increase the concentration to 180 g/L1 solutions Answer 336137 by ptaylor(2048)   on 2011-09-11 19:19:11 (Show Source): You can put this solution on YOUR website!Let x=amount of water that needs to be boiled off Now we know that the total amount of salt that exists before before x amount of water is boiled off has to equal the total amount of salt that exists after the water is boiled off. Total amount of salt before the water is boiled off is (2 liters)*90 g/l=180g Total amount of salt after x amount of water is boiled off is (2-x)liters*180g/l Soooo 180g=(2-x)180g/l 180=360-180x -180x=-180 x=1 liter Hope this helps ---ptaylor
 Age_Word_Problems/495633: Wendy was four years older than three times the age of Sammy. The sum of their ages is 60. How old is each one. We know the answers are 14 and 46, we just cant figure out the equation.1 solutions Answer 336131 by ptaylor(2048)   on 2011-09-11 19:02:41 (Show Source): You can put this solution on YOUR website!OK Let x=Sammy's age Three times Sammy's age is 3x Four years more than three times Sammy's age is 3x+4 and this is Wendy's age, sooo x+3x+4=60 subtract 4 from each side 4x=56 x=14-----------Sammy's age 3x+4=3*14+4=46---Wendy's age Hope this helps---ptaylor
 Mixture_Word_Problems/495346: 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 11% protein?1 solutions Answer 336069 by ptaylor(2048)   on 2011-09-11 13:15:54 (Show Source): You can put this solution on YOUR website!Let x=amount of soybean meal needed Then 320-x=amount of cornmeal needed Now we know that the amount of pure protein that exists before the mixture takes place has to equal the amount of pure protein that exists after the mixture takes place, sooooo: 0.16x+0.08(320-x)=0.11*320 0.16x+25.6-0.08x=35.2 subtract 25.6 from each side 0.08x=9.6 x=120 pounds----amount of soybean meal needed 320-120=200 pounds--amount of cornmeal needed CK 0.16*120+0.08*200=35.2 19.2+16=35.2 35.2=35.2 Hope this helps----ptaylor
 Travel_Word_Problems/495316: a person travels a total of 35 minutes. They jog to a location at 5 meters per second and walk back at 2 meters per second. How many total meters did they travel?1 solutions Answer 336065 by ptaylor(2048)   on 2011-09-11 13:04:22 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r Ok, lets deal in minutes: 5 meters/sec=5*60 =300 meters/min 2 meters/sec=2*60=120 meters/min Let d=one-way distance t1=time required jogging out t2=time required walking back t1+t2=35 t1=d/300 t2=d/120 d/300+d/120=35 multiply each term by 600 2d+5d=21000 7d=21000 d=3000 meters 2d=6000 meters total meters travelled Hope this helps--ptaylor
 Travel_Word_Problems/495351: Sara runs at 20 ft/sec for a half hour every day. How far does she run in miles? (note 5280 ft=1 mile)1 solutions Answer 336058 by ptaylor(2048)   on 2011-09-11 12:50:12 (Show Source): You can put this solution on YOUR website!60 sec=1 min in 1 minute she runs 20*60 ft or 1200 ft in 30 minutes, she runs 30*1200 ft=36000 ft and this equals 36000/5280= 6.8 mi Hope this helps---ptaylor
 Equations/494932: 1/2 times y divided by 3 equals 2 how do i figure out what y is1 solutions Answer 335878 by ptaylor(2048)   on 2011-09-10 15:28:01 (Show Source): You can put this solution on YOUR website!Well, we know that 1/2 times y is y/2 just like we know that 1/2 times 4 is 4/2=2 Now if we divide that by 3, we have (y/2)/3. This is a complex fraction and we can simplify it by multiplying the numerator and denominator by (1/3), like so: (y/2)(1/3)/3(1/3) and this reduces to (y/6)/1 or y/6 And we are told that this equals 2, sooooo (y/6)=2 multiply each side by 6 y=12 CK 1/2 times 12=6; 6 divided by 3=2 Hope this helps---ptaylor
 Expressions-with-variables/494923: Please solve 6r+10 = 4r+22. Thank you for your help.1 solutions Answer 335875 by ptaylor(2048)   on 2011-09-10 15:16:05 (Show Source): You can put this solution on YOUR website!6r+10=4r+22 First, subtract 4r and also 10 from each side and we get: 6r-4r+10-10=4r-4r+22-10 Next, collect like terms 2r=12 Now divide each side by 2 r=6 Now you can review the rules that allow me to do what I did CK 6*6+10=4*6+22 36+10=24+22 46=46 Hope this helps---ptaylor
 Travel_Word_Problems/494927: Two cars A and B start from a given point and travel on a straight road at average speeds of 70 km/h and 90 km/h respectively. If B starts 1 h after A find out how long before A traveled before B overtook it and the distance each traveled before they met. D=R.T d=70t d=90t d=70t+90t d=160t d/160=t1 solutions Answer 335874 by ptaylor(2048)   on 2011-09-10 15:11:01 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r ok. Looks like you gave it a shot!!! I am assuming that the cars are going in the same direction. If they were going toward each other, we would have to know how far apart they were to begin with. When car B starts, car A will have already travelled 70*1=70km. Car B will have overtaken car A when they have both travelled the same distance Let t =the amount of time needed for them to travel the same distance AFTER car B starts. Distance travelled by car A=70+70t Distance travelled by car B=90t When these distances are the same, the two cars are together, soooo: 70+70t=90t 20t=70 t=3.5 hr Distance car A travelled =70+70*3.5=315km Distance car B travelled=90*3.5=315km Hope this helps----ptaylor
 Graphs/494423: I have tried this so many times and I just cant seem to get it 0.6x+5 < 1.4x-81 solutions Answer 335637 by ptaylor(2048)   on 2011-09-09 08:05:06 (Show Source): You can put this solution on YOUR website!0.6x+5<1.4x-8 subtract 1.4x and also 5 from each side 0.6x-1.4x+5-5<1.4x-1.4x-8-5 collect like terms -0.8x<-13 multiply each side by -1 (Must now change the inequality sign) 0.8x>13 x>16.25 Hope this helps---ptaylor
 Travel_Word_Problems/494396: if i travel 22 km in 47 minutes how long would it take me to travel 37 km? Also what is the formular to work the question out? thank you1 solutions Answer 335636 by ptaylor(2048)   on 2011-09-09 07:47:58 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r So: d=rt 22=r*47 r=22/47= km/min t=d/r t=37/(22/47)=37*(47/22)=1739/22=79.045 min You can solve it by dealing with decimals instead of fractions if you like Hope this helps---ptaylor
 Rate-of-work-word-problems/494419: Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60min to paint a living room with all three working together, how long would it take Abbie if she works alone?1 solutions Answer 335635 by ptaylor(2048)   on 2011-09-09 07:38:37 (Show Source): You can put this solution on YOUR website!Let x=amount of time it takes Abbie to paint the room Then Abbie paints at the rate of 1/x rooms/min 2x=amount of time it takes Beth Beth paints at the rate of 1/2x rooms/min 3x=amount of time it takes Cathy And Cathy paints at the rate of 1/3x rooms/min Together they paint at the rate of 1/x + 1/2x +1/3x=11/6x rooms/min Now we are told that (11/6x)*60=1 (1 room, that is), or x=110 min----------------Amount of time it takes Abbie and 2*110=220 min--------Amount of time it takes Beth 3*110=330 min---------------Amount of time it takes Cathy CK In 60 min Abbie paints 60/110 of the room Beth paints 60/220 of the room Cathy paints 60/330 of the room 60/110 + 60/220 + 60/330=1 (1 room, that is) 6/11 + 6/22 + 6/33=1 multiply each term by 66 36+18+12=66 66=66 Hope this helps---ptaylor
 Travel_Word_Problems/494388: two cars are traveling in opposite directions at the rate of 60kph and 72kph. how far are they apart after 90 minutes if they depart simultaneously from the same location?1 solutions Answer 335634 by ptaylor(2048)   on 2011-09-09 05:47:12 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r Now we know that the two cars are separating at the rate of 60+72=132kph So, in 90 min (1.5hr) they are 132*(1.5)=198 km apart. Another way: In 1.5hr, car A travels 60*(1.5)=90km In 1.5hr, car B travels 72*(1.5)=108km 90+108=198km Hope this helps---ptaylor
 Travel_Word_Problems/494390: Ryan drove his car from A to B at 81 km/hr. His car broke down and he returned by bus at 54 km/hr. His total traveling time was 5 hours. How long was his trip by car?1 solutions Answer 335633 by ptaylor(2048)   on 2011-09-09 05:39:36 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r Let t1= time to travel from A to B And let t2= time to travel from B to A Now we are told that t1 + t2=5 and we know that: t1=d/81 and t2=d/54 soooooo: d/81 + d/54 = 5 multiply each term by 162 2d+3d=810 5d=810 d=162 mi t1=162/81=2 hours---------------------trip by car and t2=162/54=3 hours--------------------trip by bus Trip by car + trip by bus=5 hrs 2+3=5 5=5 Hope this helps---ptaylor
 Travel_Word_Problems/492936: Cindy's alarm clock loses 0.4 minutes in 5 hours. At this rate, how much will it lose in 14 hours 1 solutions Answer 335227 by ptaylor(2048)   on 2011-09-07 15:01:16 (Show Source): You can put this solution on YOUR website!Let x=rate per hour that Cindy's clock loses time, so: 5*x=4/10 x=4/50=2/25 minute per hour In 14 hours, then, Cindy's clock will lose (2/25)*14=28/25= 1.12 min We could also solve this problem by setting up a ratio 5 is to 0.4 as 14 is to ? Hope this helps---ptaylor
 Rectangles/492912: You have taken up gardening for relaxation and have decided to fence in your new rectangular shpaed masterpiece. The length of the garden is 4 meters and 32 meters of fencing is required to comepletely enclose it. what is the width of the garden? 1 solutions Answer 335226 by ptaylor(2048)   on 2011-09-07 14:48:51 (Show Source): You can put this solution on YOUR website!Let w=width of garden We are told that the perimeter of the garden is 32 meters and we know that the perimeter equals 2l+2w, so: 2*4+2w=32 2w=32-8 2w=24 w=12 meters Hope this helps---ptaylor
 Numbers_Word_Problems/492962: When 60% of a number is added to that number, the result is 192. What is that number? HELP? I firgot the basic algebra stuff. 1 solutions Answer 335225 by ptaylor(2048)   on 2011-09-07 14:41:50 (Show Source): You can put this solution on YOUR website!Let x= the number then 60% of x=0.60x So, we are told that: x+0.60x=192 or 1.6x=192 x=120 CK 0.60*120=72 120+72=192 192=192 Hope this helps---ptaylor
 Travel_Word_Problems/492943: Jane drove to an appointment averaging 60 mph. On the return trip, her average speed was 28 mph due to traffic, and she took 24 minutes longer. How far did she travel to the appointment?1 solutions Answer 335224 by ptaylor(2048)   on 2011-09-07 14:37:18 (Show Source): You can put this solution on YOUR website!Distance(d) equals Rate (r) times Time (t) or d=rt; r=d/t and t=d/r Let d=distance to her appointment And t=time required to travel to her appointment Then d=60t On the return trip: d=28(t+24/60)=28(t+2/5) (Lets deal in hours for the time being ) So our equation to solve is: 60t=28(t+2/5) 60t=28t+56/5 32t=56/5 160t=56 t=56/160=7/20 hr or 21 min d=60t=60*7/20 =21 mi CK at 28 mph on the return trip, it would take her 21/28 = 3/4 hr or 45 min 45-21=24 min longer Hope this helps---ptaylor
 Travel_Word_Problems/491716: how many liters of 60% alcohol solution and 40% alcohol solution should be mixed to obtain twenty liters of a 45% alcohol solution?1 solutions Answer 334746 by ptaylor(2048)   on 2011-09-05 19:17:02 (Show Source): You can put this solution on YOUR website!Let x=amount of 60% solution needed Then 20-x=amount of 40% solution needed Now we know that the amount of pure alcohol that exists before the mixture takes place is equal to the amount of pure alcohol after the mixture takes place, so: 0.60x+0.40(20-x)=amount of pure alcohol before the mixture takes place, and 0.45*20=amount of pure alcohol after the mixture takes place,so 0.60x+0.40(20-x)=0.45*20 simplify 0.60x+8-0.40x=9 subtract 8 from each side 0.20x=1 x=5 liters-------------------------amount of 60% solution needed 20-x=20-5=15 liters----------------amount of 40% solution needed CK 0.60*5+0.40*15=0.45*20 3+6=9 9=9 Hope this helps---ptaylor
 Equations/491642: a piece of lumber which is 55 inches long is cut into two parts such that 2 times the larger part will be 12 more than 5 times the smaller part. How large are each of the pieces of lumber?1 solutions Answer 334743 by ptaylor(2048)   on 2011-09-05 19:07:08 (Show Source): You can put this solution on YOUR website!Let x=the smaller part Then 55-x=the larger part Now we are told the following: 2(55-x)=5x+12 simplify 110-2x=5x+12 add 2x to and subtract 12 from each side 110-2x+2x-12=5x+2x+12-12 collect like terms 98=7x x=14 in--------------------smaller part 55-x=55-14=41 in-----------larger part CK 2 times larger part=2*41=82 in 5 times smaller part=5*14=70 in 70+12=82 82=82 Hope this helps -----ptaylor
 Age_Word_Problems/487611: In 2 years, a boy will be ¾ as old as his sister. 2 years ago, he was 2/3 as old as she. How old is the boy now?1 solutions Answer 333098 by ptaylor(2048)   on 2011-08-29 07:38:42 (Show Source): You can put this solution on YOUR website!Let x=boy's age now And let y=sister's age now We are told that: x+2=(3/4)(y+2) ---------------------eq1 We are also told that: x-2=(2/3)(y-2)----------------------eq2 simplifying eq1, we get: x+2=(3/4)y+6/4 multiply each term by 4: 4x+8=3y+6 or 4x-3y=-2------------------------------------eq1a Now we simplify eq2: x-2=(2/3)y-4/3 multiply each term by 3: 3x-6=2y-4 3x-2y=2--------------------------------------eq2a Next, we multiply each term in eq1a by 2 and each term in eq2a by 3: 8x-6y=-4----eq1b 9x-6y=6------eq2b subtract eq1b from eq2b: x=10--------------------------------boy's age now substitute x=10 into eq 1a: 40-3y=-2 -3y=-42 y=14----sister's age now CK 10+2=(3/4)(14+2) 12=12 and 10-2=(2/3)(14-2) 8=8 Hope this helps---ptaylor