Age Word Problems In Algebra - Past, Present, Future

in this video we're going to focus on solving age related word problems like the one you see on the board so Sally is three times as old as John eight years from now Sally will be twice as old as John how old is John so there's two things you need to be concerned with the present and the future so I'm going to put Sally and John so Sally's present age will call it s John's present age will call it J in the future that is 8 years from now Sally her age will be S Plus 8 she's going to be eight years older and John's age will be J + A8 so now we need to write an equation for the present and the future so at the present Sally is three times as old as John so that means s is equal to 3j now 8 years from now that is the future s will be twice as old as Sean so s+ 8 that's Sally's age in the future and she's going to be two times John's age which John in the future he's going to be J plus A8 so these are the two equations that we have and we have two variables whenever you have two variables you need two equations to solve for those two variables so let's use substitution let's replace S with 3j since s is equal to 3 J so we're going to have 3 J + 8 is equal to 2 * J + 8 on the right side let's distribute the two so it's going to be 2 J + 16 if we subtract both sides by 2J let's make some space 3j mod 2 J is J so it's going to be J + 8 is equal to 16 and if we subtract both sides by eight we will get John's age so John is 8 years old now let's find Sally's age this is John's present age by the way so John is eight Sally is three times as old as John so 8 time 3 her present age is 24 now what about in the future8 Years Later John will be 8 years older 8 plus 8 is 16 and Sally will be 8 years older 24 + 8 is 32 so as you can see in the present Sally is three times as old as John 8 time 3 is 24 but in the future she's going to be twice as old as John 16 * 2 is 32 so everything makes sense which means that the final answer is eight this is John's age at the present here's another one you could pause the video and work on it if you want to so Kim is six years more than twice Timothy's age two years ago Kim was three times as old as Timothy how old was Kim two years ago so we have the present to deal with and we also have the past instead of the future and we have Kim and Timothy which I'll just say it's Tim and we'll put the equations on this side so Kim's present age let's call it K Timothy's present age will call it t now two years ago Kim her age is going to be K minus 2 and Timothy's age two years ago is T minus 2 now what is the equation that we should write for the present at the present it says that Kim is 6 years more than twice Timothy's age so K is going to be six more six plus then twice Timothy's age so 2 * T now what about the pass two years ago Kim was three times as old as Timothy so two years ago Kim's age is K minus 2 and she was three times as old as Timothy which two years ago Timothy was T minus 2 so let's replace K with 6 + 2T since K is equal to that so 6 + 2T that's K minus this 2 is equal to 3 * tus 2 all right so we no longer need this table let's get rid of it let's combine like terms 6 - 2 is 4 and let's distribute the 3 3 * T is 3 T 3 * -2 is -6 now let's subtract 2 T from both sides so 4 is equal to 3 t- 2T which is T and now let's add six to both sides 4 + 6 is equal to 10 so Timothy is 10 years old so that's his present age now what about Kim Kim at the present it's six years more than twice to Timothy's age if you multiply age by two it's 20 and if you add six to it you get 26 so at the present Kim is 26 years old two years ago Tim was 8 years old and Kim was 24 so as you can see two years ago Kim was indeed three times Timothy's age 8 * 3 is 24 so we know these answers are correct now what is the answer to the question question how old was Kim two years ago which of these four values is the answer that we're looking for two years ago that is the past Kim was 24 so this is the answer to the question here's another one feel free to pause the video and work on this example the best way to learn is to work on the problems yourself and see if you get the right answer so try first so we have Leah and Rachel and we have the present and the future to deal with so let's make our table and let's put the equation on this side go ahead and fill the table so what should we put inside this table so Leah's present age we're going to call it l Rachel's present age is r and in the future that is 3 years from now Leah her age will be l+ 3 Rachel's Age 3 years from now will be r+ 3 now let's focus on the equations at the present Leah is 2 Less Than 3 * Rachel age so L is going to be 3 R that's three times Rachel's age less two now what about in the future 3 years from now Leah will be seven more than and twice Rachel's age so Leah in the future her current age is L + 3 and that's going to equal seven more so 7 plus twice Rachel's age so let's put a two for twice and Rachel's present age or her future age rather is not just R but it's r+ 3 so make sure you include the Plus three in the future equation now what we're going to do is we're going to replace L with what it's equal to 3 r - 2 so 3 r - 2 + 3 isal to 7 + 2 * r + 3 so go ahead and solve for R so now let's move this over here now let's combine like terms -2 + 3 is 1 so we have 3 r + 1 on the left side and let's distribute the two 2 * R is 2 R 2 * 3 is 6 now let's combine like terms 7 + 6 is 13 in our next step let's subtract two r from both sides so what we have left over 3 Rus 2 R is 1 R so 1 r + 1 is equal to 13 now let's subtract both sides by 1 so R is 13 - 1 which is 12 so this is Rachel's present age so at the present Rachel is 12 now what about Leah at the present we said that Leah is 3 * Rachel's age less two so that's 3 * 12 - 2 which is 36 - 2 that's 34 now what about in the future that is 3 years from now so 3 years from now Rachel she's going to be 3 years older she's going to be 15 and Leah is going to be 37 now if our answer is correct it has to be true for the second statement so in the future Leah will be seven more then twice Rachel's age 7 + 2 * 15 is that 37 2 * 15 is 30 30 + 7 is indeed 37 so these numbers are correct now what is the answer to the question what are we looking for so the question is asking Rachel's Age 3 years from now that means Rachel's age in the future which she's 15 so 15 is the answer to the question let's try this one so Becca is twice as old as Susan and Greg is n years older than Susan three years ago Becca was nine less than three times Susan's age how old is Greg now so we have Susan Becca and Greg we also have the present and the past to deal with so let's say PR is for present and Pa is for the pass and let's put the equations on this side so Susan's present age we're going to call it s for Becca B and G for Greg in the past that is three years ago Susan's age is s Monastery Becca's age is B Monastery and Greg's age is G minus 3 now what equations do we have in the present Becca is twice as old as Susan so B is equal to 2 Us now also in the present Greg is 9 years older than Susan so we could say G is 9 + S three years ago that is in the past Becca was nine less than three times Susan's age so B well B minus three that's Becca she was three times Susan's age so 3 * s- 3 but less 9 so minus 9 so how can we solve this we have three variables and three equations but if we focus on these two equations we only have two variables which means that we could solve for S so let's replace B with 2 s therefore 2 s - 3 is equal to 3 * s - 3 - 9 and let's write the other equation G is 9 + S so we no longer need the table so let's distribute the three 2 s - 3 is = 3 S - 9 minus another 9 -9 - 9 is -8 so 2 s - 3 is equal to 3 S - 18 now let's add three to both sides so 2 s is equal to 3 S - 15 now let's subtract 3S from both sides 2 s - 3 S is s which equal -5 so if we divide by1 s is equal to 15 now we know that Becca is twice Susan's age so Becca is 2 us so 2 * 15 is 30 and Greg is 9 + S 15 + 9 is 24 so in the the present Susan is 15 Becca is 30 and Greg is 24 now in the past three years ago Susan is going to be 12 years old Becca is 27 and Greg is 21 so now that we've listed the data on a table now we can answer the question how old is Greg now so what is Greg's present age at the present Greg is 24 so this is the answer let's try another problem where we have three variables or the age of three different people so Lauren is three less than twice Andrew's age four years from now Sam will be two more than twice Andrew's age five years ago Sam was three times Andrew's age how old was Lauren 5 years ago so we have three scenarios or three different time periods we have the present we have the future and also the pass so we're gonna have uh Andrew's H and then after that we'll put Sam's h and then Lauren and finally the last column will be for the equations now go ahead and fill in the table and solve the problem find Lauren's Age 5 years ago feel free to pause the video to do so so let's begin at the present Andrew's age will be called a Sam's age is s and Lauren's age is L now in the future that is four years from now Andrew's age he's going to be four years older so A+ 4 and Sam will be s+ 4 and Lauren will be L + 4 now in the past that is 5 years ago Andrew will be 5 years younger so a - 5 and then s - 5 and l - 5 now what about the equations the first equation is associated with the present Lauren is three less than twice Andrew's age so L is equal to 2 * Andrew's H twice Andrew's h L three now what about the Future 4 years from now we have another equation Sam will be two more than twice Andrew's age so in the future Sam is s plus4 he's going to be two more so two plus and then twice Andrew's age so Andrew in the future his age is not a but A+ 4 now what about the pass 5 years ago Sam was three times Andrew's age so five years ago Sam's age is s minus 5 and he's three times Andrew's age at the past Andrew is not a but his age is a minus 5 so this is the equation that corresponds to the pass so now what should we do at this point now that we've complet completed the table the purpose of the table is to get the equations that we need so let's write down the three equations and then we can get rid of the table so we know that s - 5 is equal to 3 * a - 5 and we also have S + 4 is = to 2 + 2 * a + 4 and also L is 2 Aus 3 so what should we do to solve it if we focus on these two equations it only has s and a so what we're going to do first is solve for a in this equation so it's s - 5 let's distribute the three so it's going to be 3 a minus 15 and now let's add five to both sides so s is equal to 3 a - 10 so now let's replace S with 3 a - 10 so 3 a - 10 + 4 is equal to 2 + let's distribute the 2 to the a + 4 so it's going to be 2 a + 8 now let's add like terms -10 + 4 is -6 2 + 8 is 10 so let's subtract 2 a from both sides so a - 6 is equal to 10 so let's add six to both sides so a is 16 so now that we have a we could find S so s is 3 * a or 3 * 16 - 10 3 * 16 is 48 48 - 10 is 38 so s is 38 now that we have S we can calculate or now that we have a we can calculate l so using this equation L is going to be 2 * a or 2 * 16 - 3 2 * 16 is 32 32 - 3 is 29 so this is L so now let's organize the answers into a table so we have the present the future and the past at the present Andrew is 16 and Sam is 38 and Lauren is 29 so we can get rid of this in the future that is four years from now Andrew is going to be 20 Susan is going to be 42 Lauren is going to be 33 in the past five years ago Andrew was 16 - 5 or 11 Susan was 38 - 5 or 3 3 and Lauren 29 - 5 was 24 so now what is the answer to the question how old was Lauren 5 years ago in the past 5 years ago she was 24 so this is the answer here's another one Gabby is one year more than twice Larry's age three years from now Megan will be 27 less than twice Gabby's age 4 years ago Megan was one year less than three times Larry's age how old will Megan be 3 years from now so we have the present the future and also the pass so in the First Column let's put Larry in the second column let's write Megan in the third column we're going to put in Gabby and for the last column this is going to be the equations so Larry's present age is L Megan's present age is M Gabby's present age is G now three years from now that is in the future everyone is going to be three years older Larry's going to be l+ 3 Megan m+3 Gabby G+ 3 four years ago in the past everyone will be 4 years younger so L -4 m-4 and gus4 now let's write the equations so let's focus on the present Gabby is one year more than twice Larry's age so Gabby G is twice Larry's age plus one now what about 3 years from now Megan is 27 less than twice Gabby's age so 3 years from now Megan is going to be m+ 3 and she's twice Gabby's age which is 2 and Gabby's Gabby's present age is G plus three in the future so she's twice that less 27 now what about in the past four years ago Megan was one year less than three times Larry's age so in the past Megan is M4 and she's going to be three times Larry's age and in the past Larry is L minus 4 so she's three times his age less one so now that we've have now that we have the three equations we don't need the table anymore so let's write the three equations first so m + 3 is equal to 2 * G + 3 - 27 N - 4 is = to 3 * l - 4 - 1 and also G is 2 L + 1 so we have three equations and three variables let's solve the system of equations so in this equation I'm going to get M by itself so let's distribute the two first so m + 3 is equal to 2G + 6 - 27 so m + 3 is equal to 2G 6 - 27 is -21 and now let's subtract three from both sides so m is equal to 2G minus 24 so I'm going to save this equation in this upper right corner we're going to use it later so in this equation I'm going to isolate M again so M minus 4 let's distribute to 3 it's going to be 3 l -2 - 1 -12 - 1 is -3 now let's add four to both sides so m is equal to 3 l -3 + 4 is9 so since I have two equations that both equal m I could say that 3 l - 9 is equal to 2 g - 24 and now since I have G in terms of L I'm going to replace G with 2 L + 1 so 3 l - 9 is equal to 2 * 2 L + 1 - 24 so that's 3 l - 9 is equal to Let's distribute the two so it's going to be 4 L + 2 - is 24 2 - 24 is -22 and now let's add nine to both sides actually let's add 22 to both sides -9 + 22 or 22 - 9 is 13 now let's subtract 3 l from both sides so 13 isal Al to 4 lus 3 l which is L so L is 13 so that's how old Larry is at the present so now that we have Larry's age we could find Gabby's age so Gabby is 2 L + 1 so that's 2 * 13 + 1 2 * 13 is 26 + 1 that's 27 so Gabby is 27 years old at the present so now let's find out how old Megan is so Megan is using this equation it's 3 l - 9 so that's 3 * 13 - 9 3 * 13 is 39 39 - 9 is 30 so Megan is currently 30 now if we use the other equation we should get the same answer if we use this equation so m is equal to 2G minus 24 if we get a different answer then something is wrong Gabby's age is 27 2 * 27 is 54 54 minus 24 is 30 so Megan is indeed 30 at the present so this is going to be the present the future and the past so at the present Larry is 13 Megan is 30 and Gabby is 27 now let's fill in the rest of the table in the future that is 3 years from now everyone is going to be 3 years older so 13 + 3 is 16 30 + 3 is 33 27 + 3 is 30 now in the past that is four years ago everyone is four years younger relative to the present so 13 - 4 is 9 30 - 4 is 26 27 - 4 is 23 so we have everything now now we could find the answer to the question so what do we look looking for in this problem what is the answer the question is this how old will Megan be 3 years from now so that question does it pertain to the past the present or the future it's three years from now so that's the future so Megan is going to be 33 years um of age three years from now right now at the present she's 30 but 3 years from now she'll be 33 so 33 is the answer to the problem so now you know how to figure out these past present future age related problems so that is it for this video thanks for watching I hope you found it to be educational and uh that's it I hope you do well on your tests and have a great day

Channel: The Organic Chemistry Tutor

Views: 583,566

Keywords: age word problems, age word problems in algebra, algebra, prealgebra, two variables, three variables, past present future, system of linear equations, math, elimination method, substitution, linear equations, age problems algebra, age problems tricks and shortcuts, age problems tricks, college algebra, past, present, future, age, problems, practice, examples, word problems

Id: 7x7Hl9ztYbk

Length: 35min 18sec (2118 seconds)

Published: Sat Nov 12 2016