The problem is poorly worded. It says that in 4 years Ann will be twice as old, but does not say twice as old as the brother. Stating this clearly makes the problem much easier. This way you are not floundering around with Ann going from 3X to 6X and trying to figure it out from there.
If you're going to pick holes in the wording, a more obvious criticism is where he says "Ann is 3 times older than her brother". That should really be "Ann is 3 times as old as her brother".
my first encounter with "word" problems was converting to equations. And this is the essence of engineering... Combine with the general observation that to find two unknowns requires two equations. [In the beginning we have solved One equation in One unknown.] here: Two unknowns A: Ann's age B: Brother's age Two equations: eq.1: Ann is 3x Brothers age A = 3B eq.2: In four years A = 2 × B A+4 = 2(B+4) A+4 = 2B + 8 A = 2B + 4 solve two equations... there's several methods that could be tried and experience with all of them yields easiest, less messy way of solving A = 3B eq.1 A = 2B + 4 eq.2 What I see.. A = A or A = 3B = A = 2B + 4 3B = 2B + 4 B = 4 sol.1 A = 3B eq.1 A = 3(4) A = 12 sol.2 VERIFY eq.1 A = 3B ? 12 =? 3(4) 12 =❤ 12✔️ eq.2 A+4 = 2(B+4)? 12+4=?2(4+4) 16 =? 2(8) 16 =❤ 16✔️
This problem can be solved employing a system of linear equations. Given Ann is the variable "x" and her brother is the variable "y." x - 3y = 0 (x+4) - 2(y+4) = 0 x+4 - 2y -8 = 0 x - 2y = 4 -(x - 3y = 0) -x + 3y = 0 y = 4 Accordingly, Ann's brother is 4-years old.
Your answer looks great; however, you always want to show your work. On an exam, if your answer is incorrect, the examiner will likely grant you partial credit for your work. You can also study where your thinking went awry as well. In truth, the only valuable math problems are those one gets wrong because those are the only ones one learns from.
lets try to solve this ambiguous age word puzzle. 'she will be twice as old' Refers to what, twice her own age or her brother’s age. --------------------------------------------------------------------------------------------- let age of brother = y let age of Ann is 3 times older than brother --> 3 x y = 3y in 4 years Ann's age will be --> 3y + 4 in 4 years brother's age will be --> y + 4 Given that Ann's age will double in 4 years compared to Brother's --> 3y + 4 = 2[y +4] 3y + 4 = 2y + 8 3y - 2y = 8 - 4 y = 4 So, brother's age was 4 years before 4 years ago And Ann's age was 3y = 3 x 4 = 12 at that time after 4 years: brother's age was y + 4 = 4 + 4 = 8 years Ann's age was 3y + 4 = 3[4] + 4 = 12 + 4 =16 years , 16 is twice the age of 8
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The problem is poorly worded. It says that in 4 years Ann will be twice as old, but does not say twice as old as the brother. Stating this clearly makes the problem much easier. This way you are not floundering around with Ann going from 3X to 6X and trying to figure it out from there.
If you're going to pick holes in the wording, a more obvious criticism is where he says "Ann is 3 times older than her brother". That should really be "Ann is 3 times as old as her brother".
my first encounter with "word" problems was converting to equations. And this is the essence of engineering...
Combine with the general observation that to find two unknowns requires two equations. [In the beginning we have solved One equation in One unknown.]
here:
Two unknowns
A: Ann's age
B: Brother's age
Two equations:
eq.1: Ann is 3x Brothers age
A = 3B
eq.2: In four years A = 2 × B
A+4 = 2(B+4)
A+4 = 2B + 8
A = 2B + 4
solve two equations...
there's several methods that could be tried and experience with all of them yields easiest, less messy way of solving
A = 3B eq.1
A = 2B + 4 eq.2
What I see.. A = A
or
A = 3B = A = 2B + 4
3B = 2B + 4
B = 4 sol.1
A = 3B eq.1
A = 3(4)
A = 12 sol.2
VERIFY
eq.1 A = 3B ?
12 =? 3(4)
12 =❤ 12✔️
eq.2 A+4 = 2(B+4)?
12+4=?2(4+4)
16 =? 2(8)
16 =❤ 16✔️
This problem can be solved employing a system of linear equations.
Given Ann is the variable "x" and her brother is the variable "y."
x - 3y = 0
(x+4) - 2(y+4) = 0
x+4 - 2y -8 = 0
x - 2y = 4
-(x - 3y = 0)
-x + 3y = 0
y = 4
Accordingly, Ann's brother is 4-years old.
A = 3B and A+4 = 2(B+4) so 3B + 4 = 2B + 8 resulting in B = 4 yo and A = 3B = 12 yo
Her brother is 16 months old, if she is 3 times his age and in 4 years, she will be twice the age she is now.
assuming that ann isn't born yet, the older brother is 12yrs old...
(1) a = 3b
(2) a + 4 = 2(b + 4) = 2b + 8
From (1) a + 4 = 3b + 4
Therefore:
3b + 4 = 2b + 8
b + 4 = 8
b = 4
3x+4= 2(x+4)
3x+4=2x+8
3x-2x= 8-4
X=4
Her brother is 4 and she is 12
In 4 years he will be 8 and she will be 16.
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Your answer looks great; however, you always want to show your work. On an exam, if your answer is incorrect, the examiner will likely grant you partial credit for your work. You can also study where your thinking went awry as well. In truth, the only valuable math problems are those one gets wrong because those are the only ones one learns from.
got 4 took a bit for the equations thanks for the fun
2(x + 4) = 3x + 4
2x + 8 = 3x + 4
x + 4 = 8
x = 4
lets try to solve this ambiguous age word puzzle.
'she will be twice as old'
Refers to what, twice her own age or her brother’s age.
---------------------------------------------------------------------------------------------
let age of brother = y
let age of Ann is 3 times older than brother --> 3 x y = 3y
in 4 years Ann's age will be --> 3y + 4
in 4 years brother's age will be --> y + 4
Given that Ann's age will double in 4 years compared to Brother's --> 3y + 4 = 2[y +4]
3y + 4 = 2y + 8 3y - 2y = 8 - 4
y = 4
So, brother's age was 4 years before 4 years ago
And Ann's age was 3y = 3 x 4 = 12 at that time
after 4 years:
brother's age was y + 4 = 4 + 4 = 8 years
Ann's age was 3y + 4 = 3[4] + 4 = 12 + 4 =16 years , 16 is twice the age of 8
Wait, didn't Abbott and Costello incorporate a version of this problem in their stand-up?
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