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Dan is 6 years older than Ann. In two years, he will twice as old as Ann. Dan is how old now?
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- čas přidán 21. 02. 2024
- How to solve an algebra age word problem - linear equations.
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No need for any equations. Start from the possible answers. Pick any one. It takes just a moment to see if it is too high, too low, or just right. Either you got the answer or you know which possible answer to check next. Took me a total of under 10 seconds.
Having the 4 possible answers makes it easy as you can work back, but it takes a bit of thinking to actually work it out.
Nobody cares that you figured out the answer in "under 10 seconds" because it's a very simple problem and, more importantly, the goal is not getting the result but rather to provide some instruction in building and solving Algebraic equations. But it's so cool that you got the answer. Good job.
I used the same process but it took me a good minute
The actual answer d) 10 did not show on my screen till the very end of the video but I used the deductive method also. This was a good refresher though. The instructor did state the answer at the beginning.
Plug in
I love watching your videos to relax. The old saying, "Use it or loose it," really does apply to Math.
I love your videos. You explain math in very easy terms! I was in honors math in high school but forgot a lot of it in the last 50 years, but you make it easy to bring it all back.
This is one of the best Maths teacher but I need to buy time to sit down and watch his videos.
one of the best math teachers on utube is " the organic chem tutor"..........clear and succinct
I started at Ann being 0 and Dan being 6 and added 2 to each figure and came to 2 and 8. Thereafter i continously added 1 to both 2 and 8 until i reached 6 and 12 and worked. 2 years back and came to 4 and 10. Done mentally. No pen, paper or equations necessary. Done under a minute
Just use the answers they are there to limit choices and save time. Wast of time plugging in unknown variables when there are 4 known variables. Took 10 seconds honestly.
Me too
I did it differently.
Dan is 6 years older, so when Ann is 6 and he is 12, then he is twice as old as Ann,so 6x2.. but he won't be twice as old in 2 years, so 6x2-2
Actually, if Ann is now 4 and Dan is now 10, he is now 'more' than twice as old as Ann. He doesn't become exactly twice as old as Ann until Ann is 6 and Dan is 12. So, the answer is Dan is twice as old as Ann when Dan is 12.
Or, until Dan is 12 and Ann is 6, he will be 'more' than twice as old as Ann.😊.
This problem requires two variables, Ann and Dan, to express the age relationships.
Initially it is given that: 1. Dan (D) is six years older than Ann (A). 2. In two years Dan will be twice as old as Ann.
1. D = A + 6 present age
2. D = 2A + 2 future age
Rearrange formulas such as now A is the dependent variable.
1. A = D - 6 present age
2. A = (D - 2)/2 future age
Now combine the two equations to find the age of Dan
D - 6 = (D - 2)/2 multiply both sides by two to eliminate the fraction
2 * (D - 6) = D - 2 multiply the left side by 2
2D - 12 = D - 2 add 12 to both sides
2D = D + 10 subtract D from both side to get the final answer.
D = 10
nice
Now that I can follow 👍
Easier
D=2A+2
D=A+6
Subtract
0=A-4
A=4, D=6
Yes, that is essentially the way I approached it. Except I went:
Let d be Dan's present age. Let a be Ann's present age.
1) d - 6 = a
2) d + 2 = 2a
Substituting expression for a from equation 1) into equation 2) gives:
d + 2 = 2(d - 6)
= d + 2 = 2d - 12
= - d + 2 = - 12
= - d = - 10
= d = 10.
I did get stuck initially as I wanted to add 2 years to Ann's age as well. Thus for equation 2) d + 2 = 2a + 2. But this yields the wrong answer. Then I realised that d is the dependent variable (I think?), and the two years have already been added on the left-hand side. In other words, in two year's time Dan's age is simply twice Ann's age. No need for adding the 2 to the right-hand side.
You only need to use one variable as is shown in the video. It's a much cleaner way to solve problems such as this.
x = Ann's current age & x+6 = Dan's current age. x+2 = (x+8)/2 → 2x+4 = x+8 → x+4 = 8 → x = 4 , Therefore x+6 = 4+6 = 10. QED
Overkill!
Got it! Because I worked out how each of the multiple choice answers worked out.
I'd use A and D for variable letters
Let D = Dan; Let A-= Ann; D-6=A; ergo: D=A+6; D+2=2(A+2) substitute A+6 for D and we get A+6+2=2(A+2); simplify: A+8 = 2A+4; Subtract A from both sides and we get 8=A+4; 4=A, ergo D=10 The answer is D.
I am a Grandparent and have told my children to view your CZcams for help with their children's Math problems! P.S. The green chalkboard brings back great memories of K-12!!
A problem I had in school was that I could never show my work as I always, as I did here, solve the problem in my head to get the right answer in about 15 seconds. I would then test out my answer by doing basic math with no intervening steps shown as it was done intuitively in my head.
I had the same issue but my teacher said I either did it her way or a failing grade was on the horizon. I never did it her way but i almost always had the correct answer- it was odd
Love the two variable, two equation word problems...
unknowns:
Ages:
Dan : D
Ann : A
equations:
D = A + 6 eq.1
D + 2 = 2×(A + 2) eq.2
D = -2 +2A + 4
D = 2A + 2 eq 2.1
collect formulas
D = A + 6 eq.1
D = 2A + 2 eq.2.1
subtract eq 2.1 from eq.1
0 = -A + 4
A = 4 sol.1
continue
D = A + 6 eq.1
A = 4
D = 4 + 6
D = 10 sol.2
Collect solutions
A = 4 sol.1
D = 10 sol.2
VERIFY
D =? A + 6 eq.1
D =? 2A + 2 eq 2.1
with
A = 4 sol.1
D = 10 sol.2
D =? A + 6 eq.1
10 =? 4 + 6
10 =❤ 10✔️
D =? 2A + 2 eq 2.1
10 =? 2(4) + 2
10 =? 8 + 2
10 =❤ 10✔️
I think Dan should be 10 now and Ann is 4…
yes in two years she'll be 6 and he'll be 12 which makes him half as old.
@@DeeDee-mv2uw😢😮Ý
When would you use this in every day life. Only in school math class.
Good instructor overall👍
Greetings. Dan is presently 10 years old. These were my absolute favourite problems in studying algebra. Now for the solution. We will start by assigning the value X to represent Ann's age. Now, when Ann is X years old, Dan will be (X+6) since he is 6 years older. Moving forward, in 2 years time, Ann and Dan will all be 2 years older. That is Dan's age will (X+6+2) years, and Ann's age will be (X+2). Using the information that after 2 years are added to their initial ages Dan's age will be twice Ann's age, we have
(X+6+2)=2(X+2). Solving for X gives
X=4. Therefore, Dan's current age is
(4+6) years, equals 10 years old.
When Dan was 10, Ann was 4 and in 2 years, Dan would have become 12 while Ann would have become 6 making Dan twice as old as Ann after 2 years.
Someone commented on a previous problem and made a snarky comment which made me laugh. I am 75 and you can teach old dogs new tricks. I decided to see if I followed this site could I refresh or learn math skills. I was terrible in math and struggled all my life. I am not going to deal with algebra too much or geometry but I have made some improvements on the simple basic stuff just by doing these problems. Now it is fun to challenge myself because I don’t have Sister Mary Joseph standing over me sternly chastising me. Lol
Let dans age = d and let anns age = a,
therefore d=a+6..... equation i
and also d=2a+2 in two years time...... equation ii
Now subtract ii from i
We have d-d=a+6-(2a+2)
0=a+6-2a-2
Or a=4= anns age
Substitute a in equation i
d=4+6.
d=10=dans age
Therefore answer is d......QED
Figured out an algebraic equation
2(A+2)=(A+2) + 6
Ann = 4
Dan = 10
Answer:@1:53
6 to be twice her age is at least 12 -2 years means he is 10 now with logical reasoning without all the math gymnastics. 🤣🤣🤣🤣
I’m with ya %100 !! And that’s my math !! 🤣🤣
Reading comments..SO MANY OF U make this sound so hard.. NOW think of the age range this is meant for..NOW give ur results..!!!
Now, let Ann' age is x, thus Dan's age is x+6.
Next 2 yrs, Ann age is x+2 and Dan age (x+6)+2.
And Dan age is twice of Ann
2(x+2)=(x+6)+2
x=4.
This is the first one i got right. he gave us 4 'answers', process of elimination.
Dan is officially 6years and 1 minute old to be twice Ann’s age !! That’s the real answer no matter what the given choices are !!😂 19:26
This seemed a complicated approach to me. Wouldn't it be simpler ttook do it this way:
Dan is 6 years older than Ann, therefore he was 6 when Ann was born.
This means Ann would have to 6 for Dan to be twice her age making him 12 At that time.
As this won't happen for another 2 years, Dan is currently 12 years - 2 years, so Dan is 10
Your reasoning is correct but the point is learning how to use algebra to solve problems like this
@@ellentronicmistress4969the purpose of maths is to come to a solution; not to make it so complicated as to make people scared of it and think it is out of their reach. Make others think it is achievable at least.
@@elisefoad2326 Maths teaching today is as much aboutwhy things work. and not just how to make them work. It's not just about teaching short-cuts and actually the opposite to your assertion is true in my opinion, because teaching children properly helps them to understand the subject more and thus they enjoy it more.
got it.... calculate or substitute using answer options thanks for the fun.
Dan is 6 years old now and Ann is 2.
Mmm, looks like algebra to me... I can see 4 equations:
(1) D1 = A1 + 6 (D1 is the one we are looking for !)
(2) D2 = D1 + 2 = (A1+6) + 2 = A1 + 8 so A1 = D2 - 8
(3) A2 = A1 + 2 so A2 = (D2-8) + 2 = D2 - 6
(4) D2 = A2 x 2 so D2 = (D2-6) . 2 so D2 = 2D2 - 12 and D2 = 12 yo
D1 = D2 - 2 so D1 = 10 yo so the answer is D...
I like algebra !
I did this and got the answer (×+6)+(x-6)=2(×2+2) raise to power 2
×=2(×+2)raise to power 2
=8+2 years =10years
You added a long drawn out solution to a problem most people can solve in their head in seconds
He showed the correct way to solve it using algebra. Many people are just starting their algebra journey and these videos are for them.
And for the sake of those who could not solve it in seconds, John, graciously explain step by step. So thank you John!!
I apologize I miss spoke
D 10 years by cheating using process of elimination.
I'll have to watch the algebraic solution.
It isn’t cheating to go through the answers in multiple choice questions and figure which one works. D in this case.
Dan is 10 . X+6 is Dan ann is x. In two yrs Dan is x+6+2 and Ann will be x+2. Equation is x+6+2=2(x+2) and solve. X is 4
10. I just plugged in all the answers. 10 is the only option that works.
A more interesting question might be, How old will Dan be when he figures out how to solve this problem?
D = A + 6 ---> A = D - 6
In 2 years
D + 2 = 2 (A + 2)
D + 2 = 2A + 4
D = 2A + 2, and A = D - 6, thus
D = 2(D - 6) + 2
= 2D - 12 + 2
D = 2D - 10
10 = 2D - D
10 = D
D 10. I just could see in my head the correct answer without doing an equation.
Why use X
Why not use "D" for Dan's current age and "A" for Ann's current age.
Mainly for those beginning algebra
D. Final answer.
At the title card, my answer is d) 10.
If Dan is 10 now, then Ann is 4. Add 2 years, and Dan is 12, with Ann being 6.
None of the other options work out.
Dan is 6 yrs older than Ann; D=A+6;
In two years; (D+2); (A+2);
Dan will be twin as old as Ann; D+2=2(A+2);
Since D=A+6; therefore (A+6)+2=2A+4 ;
A+8=2A+4;
8=A+4; eliminate the A's form both sides;
How old is Dan now? 4=A; Since Dan is 6 yrs older than Ann right now; Dan is 10!
His is twice 6 in two years.
Equation. DAN
6x2=X+2
12 = X+2
DAN =10
ANN = 10-6
√8 2^3 (x+2x-3)
Dan is 6 years older than Ann ... so their ages are X and X + 6
In two tears he will be twice as ald ... X + 6 + 2 = 2 (X + 2)
X + 8 = 2X + 4
8 - 4 = 2X - 2
4 = X
Ann is 4 Dan is 10 and in two years they will be 6 and 12
10 years old now
So much fun!
Even if it is a leap year you woulde just added one +2 =equals three =nine years old
Dan is 10yrs now and Ann is 4. In two years he will be twice the age of Ann which is 12 and Ann will be 6.
I got the right answer by reading and thinking. But knowing i failed because I don’t have the problem written out. By watching your way didn’t help me cause that’s not the way i thought out the problem. And I couldn’t figure out how to write out what was in my head. Crap.
Let's just pause to realise that they both have the same birthday and it is whenever you read this question.
I think some of you are missing the point. He is teaching us how to solve a simple word problem using algebra so that when you have a more difficult problem, you know how to solve it.
I only get 8 can’t see it any other way but I’ve failed simple maths last try in my early sixtys
15:31 in the video?
Dan is 10 years old while Ann is 4, in two years Dan will be 12 while Ann will be 6. That makes Dan double Ann's age
12. 4 and 10 yrs old in 2 year 6 and 12 yr old.
15:32 "x is equal to 8" oops
Practice = Skill
So the comment that people leave with the math situation they don’t realize how many people is out there have issues with mathematics and I am one of them
The answer is 10. Because she is 4. Inb2 years Ann will be 6 and Dan will be 12.
What a long drawn out way of solving a very simple problem.
10yrs old
d) 10 i knew within a few seconds, but then again i'm an 11th grade student
That's a trick question how old is Ann?
😂😂😂😂😂 he does talk sooooo much I hope he has real friends
Dan is 10
D=A+6, D=2A-2 2A-2=A+6 A=4, D=4+6=10 Why must we make things complicated?
D=2A - 2 is incorrect
should be
D + 2 = 2(A + 2)
D = 2(A+2) - 2
D = 2A + 2
Not making X be Dan's age is seting yourself up for failure. Whats wrong with making X be the requested answer?
10 years
Just ask Dan.
Dan 10 yrs, Ann 4yrs.
It's always the last answer so therefore Dan is 10
6 and Ann is 2 and in 2 years he will be 8 and she will be 4.
10 years of age,d)
Dan is 12 yrs
Ann is 6yrs
John the JACKASS, who makes mountains out of molehills
I wonder who's stupid enough to not get the answer within seconds but still intelligent enough to understand your explanation.
That is really not nice to say who stupid because if you don’t understand math, you don’t understand what you’re talking about
Easy enough to figure out in your head. In 2 years Dan will still be 6 years older than Ann. If he is twice as old as Ann at that point, then Dan has to be 12 and Ann has to be 6. Back up 2 years to get the current ages.
My equation: X+2=6(2)...my answer 10.
Not watching the video or reading the comments. 6+2=2x ---- 4 = x ---- 4+6=10 ---- 10+2 = 12 Dan is 10 and Ann is 4.
D) 10
let his age be A
(A + 2) ÷ 2 = 6
A + 2 = 12
A = 10
78 and half
ANN's is 6years old Dan is 8 year's old
If Ann is 4, Dan can't be 10 because it says that Dan is TWICE as old as Ann. 10 is not twice as much as 4...
I thought it was only me finding this hold thing strange 😂.
Ok so the trick is this right now he is not twice as old as her...but in two years time then that will happen .Which means if she is 4 now 2 years time she will be 6 and 6 times 2 is 12 ...which will be Dan's age ....I was totally mentally screwed 😅
but 12 is twice the age of 6 in 2 years
d. -10 years
I was always good at solving problems, but not so good at proofs. I can give you the answer, but I cannot tell you why. I guess my brain is wired differently.
Before the /2 years Dan is 10vnow
D=A+6
D+2=2(A+2)
Then there's no need to remember that x=A
Geeze
Please don't get stuck in using the classic variables x, y, etc.
He is 10.
Yes 10
Response : d) 10
8 i believe.
D=10
I cant help but think you complicate things
Because we have the possible answers given, this is too easy. It took me about 1 minute to find the correct answer. I'm 78 and obviously decades and decades removed from formal classroom math. The video explanation is "extremely" confusing to me as I followed along this math teacher's algebraic calculations. No doubt with a more complicated problem, algebra is "the" key to the solution...but for this extremely easy story problem (given the answer), common sense finds the answer in less than a minute.
a) 12
12 Year old