Problem : What are our ages now?

Question

Problem :

My age was twice your age , when I was the

same age as yours now. And when you are the

same age as mine now , the sum of our ages is

$63$ .

What are our ages now?

I see this problems in my teacher and solution is

$(28,21)$

But I don't know how I solve it !

Please if any one have ideas drop here to see

Thanks!

I think that's much better :) – postmortes Oct 14 '19 at 06:17 — postmortes, Oct 14 '19 at 06:17

Certainly not a dog · Answer 1 · 2019-10-14T08:31:11.887

4

Let your age be $x$. If the age difference is $\Delta x$, in $\Delta x$ years our ages will sum to 63, so we have $2x+\Delta x = 63$, which is to say $\Delta x = 63-2x$.

We also know that $\Delta x$ years ago you were twice my age, so $x-\Delta x = 2(x-2\Delta x)$ or $3\Delta x = x$.

$$3\cdot 63 -6x = x$$ $$\implies x = 27$$ $$\implies \Delta x = 63-54 = 9$$ $$\implies\boxed{\text{You are 27, I am 18}}$$

So there seems to be a miscalculation by your teacher. (Obviously the reasoning is instructive but just to confirm, $9$ years ago you were $18$ and I was $9$, hence satisfying the first statement, and in $9$ years you will be $36$ and I will be $27$ meaning our ages will indeed sum to $63$)

edited Oct 14 '19 at 08:31

answered Oct 14 '19 at 06:19

Certainly not a dog

1,452

Thanks! Can you explain to me this step! $x-∆x=2(x-2∆x)$ how ? – Ellen Ellen Oct 14 '19 at 06:46
My age is $x-\Delta x$, so $\Delta x$ years ago my age was $x-2\Delta x$. Your age at that time, $x-\Delta x$ was twice mine. Hence that equation. – Certainly not a dog Oct 14 '19 at 06:51
2

The teacher's solution is assuming "My age is twice your age ..." i.e. $x = 2(x-2 \Delta x) \Rightarrow x = 4 \Delta x$ and so $\Delta x = 7, x = 28, x- \Delta x = 21$. – gandalf61 Oct 14 '19 at 14:43
The question says "was" :| – Certainly not a dog Oct 14 '19 at 16:17

85579 · Answer 2 · 2019-10-14T06:54:10.240

My age was twice your age, when I was the same age as yours now. [...]

a - x = 2 (b - x)  ←  a - x = b

x is some years ago
a is my current age
b is your current age

[...] And when you are the same age as mine now, the sum of our ages is 63.

a = b + y  →  a + y + b + y = 63

y is some years from now

Solve a system with four equations and four variables; solution should be unique.

System solution (spoiler):

a = 27, b = 18, x = 9, y = 9

Source: https://www.mathportal.org/calculators/system-of-equations-solver/system-4x4.php using matrix: [1, -2, 1, 0; 1, -1, -1, 0; 1, -1, 0, -1; 1, 1, 0, 2;] at the LHS of the equation and vector column [0; 0; 0; 63;] at the RHS of the equation.

Problem : What are our ages now?

2 Answers2