# Thread: Word Problem And Equation

1. ## Word Problem And Equation

I have two problems right now the 1st is an equation

1, Two people walk 240 meters at a constant speed
Person A takes 100 more steps than the other,
Person B's steps are 20cm longer, Find how mant steps they take

2. I did most of the problem but I can't get any farther on this
9(u^2+uv+v^2)=7(u+v)^2
u=2^(x+y)
v=3^(x-y)

The orignal problem is
Solve System
4^(x+y)=27+9^(x-y)
8^(x+y)-21*2^(x+y)=27^(x-y)+7*3^(x-y-1)

2. Originally Posted by AHDDM
I have two problems right now the 1st is an equation

1, Two people walk 240 meters at a constant speed
Person A takes 100 more steps than the other,
Person B's steps are 20cm longer, Find how mant steps they take

...
Hello,

let the number of steps of A be: x
let the number of steps of B be: x - 100

let the length of one step of A be: y
let the length of one step of B be: y + 0.2

Then you have:

$\displaystyle A:\ x \cdot y = 240~\implies~\boxed{y=\frac{240}{x}}$

$\displaystyle B:\ (x-100)(y+0.2)=240$ . Substitute y by the term of the equation A:

$\displaystyle (x-100)\left(\frac{240}{x}+0.2\right)=240$

I'll leave the rest for you.

3. Originally Posted by AHDDM
2. I did most of the problem but I can't get any farther on this
9(u^2+uv+v^2)=7(u+v)^2
u=2^(x+y)
v=3^(x-y)

The orignal problem is
Solve System
4^(x+y)=27+9^(x-y)
8^(x+y)-21*2^(x+y)=27^(x-y)+7*3^(x-y-1)
It looks like your approach is right, though I'm not sure where you got that u, v equation from.

$\displaystyle 4^{x+y}=27+9^{x-y}$
and
$\displaystyle 8^{x+y}-21*2^{x+y}=27^{x-y}+7*3^{x-y-1}$

Let's rewite these:
$\displaystyle 2^{2(x+y)} = 27 + 3^{2(x-y)}$
and
$\displaystyle 2^{3(x+y)} - 21*2^{x+y} = 3^{3(x-y)} + \frac{7}{3}*3^{x-y}$

Let $\displaystyle u = 2^{x + y}$ and $\displaystyle v = 3^{x - y}$.

Then we have
$\displaystyle u^2 = 27 + v^2$
and
$\displaystyle u^3 - 21u = v^3 + \frac{7}{3} \cdot v$

As the graph below shows (use x = u and y = v) you are done. The graphs do not intersect, so there are no solutions.

-Dan

4. for the word problem I am getting to x^2-100x-12000=0 and from there no logical solutions coming out and it doesn't come out cleanly from quadratic formula

5. Originally Posted by AHDDM
for the word problem I am getting to x^2-100x-12000=0 and from there no logical solutions coming out and it doesn't come out cleanly from quadratic formula
$\displaystyle x^2 - 10x - 12000 = 0$