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# How Old Are They Now?

## Question

Eight years ago, Verizon Wireless was half as old as Sprint will be when Sprint is one year older that AT&T will be five times as old as AT&T will be two years from now.

Ten years from now AT&T will be twice as old as Sprint was when Verizon Wireless was nine times as old as AT&T

When AT&T was one year old, Verizon Wireless was three years older than AT&T will be when Sprint is three years older than AT&T will be when Sprint is there times as old as Verizon Wireless was six years before the time when Sprint was half as old as AT&T will be when Verizon Wireless will be ten years older than Verizon Wireless was when Sprint was one-third as old as AT&T will be when Verizon Wireless will be three times as old as it was when Sprint was born.

How old are they now?

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Ages now: AT&T=A; Sprint=S; Verizon Wireless=V.

Eight years ago, Verizon Wireless was

half as old as Sprint will be when Sprint is

one year older that [than?] AT&T will be [when it is?]

five times as old as AT&T will be two years from now.

[V-8] = 1/2 [1 + 5*(A+2)]

Ten years from now AT&T will be

twice as old as Sprint was

when Verizon Wireless was nine times as old as AT&T let x satisfy [V-x] = 9[A-x]

[A+10] = 2[s-x]

When AT&T was one year old, let u satisfy [A-u] = 1

Verizon Wireless was three years older than AT&T will be let z satisfy [V-u] = 3 + [A+z]

when Sprint is three years older than AT&T will be let w satisfy [s+z] = 3 + [A+w]

when Sprint is there [three?] times as old as Verizon Wireless was let y satisy [s+w] = 3[V-y]

six years before the time when Sprint was half as old as AT&T will be let q satisfy [s-(6+y)] = 1/2[A+q]

when Verizon Wireless will be ten years older than Verizon Wireless was let t satisfy [V+q] = 10 + [V-t] -> q = 10-t

when Sprint was one-third as old as AT&T will be let m satisfy [s-t] = 1/3[A+m]

when Verizon Wireless will be three times as old as it was when Sprint was born. [V+m] = 3[V-S] -> m= 2V-3S

How old are they now?

Eleven variables: A, S, V, x, u, z, w, y, q, t, m

Eleven equations:

[ 1] 2[V-8] = 1 + 5[A+2]

[ 2] V-x = 9[A-x]

[ 3] A+10 = 2[s-x]

[ 4] A-u = 1

[ 5] V-u = 3 + A+z

[ 6] S+z = 3 + A+w

[ 7] S+w = 3[V-y]

[ 8] 2[s-6-y] = A+q

[ 9] q=10-t

[10] 3[s-t] = A+m

[11] m = 2V-3S

piece of cake.

Back later with the solution.

If you're reading this and this is the latest post, have a crack at them.

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Wondering what happened to the spoiler tag in previous post, and why I can't edit it to fix.

First statement in OP is not a well formed sentence, so it's meaning is not certain.

Eight years ago, Verizon Wireless was half as old as Sprint will be when Sprint is one year older that AT&T will be five times as old as AT&T will be two years from now
So the 11 equations in previous post are uncertain as well.

They reduce to

13A -8S -V = -40
6A -16S +8V = -60
`5A	 - 2V = -27`

which have the unlikely solutions

S = 64/11

A = 21/11

V = 201/11

Which is where I'll leave it, as I have dinner to eat. It's solved in principle.

Which is to say,

A, S and V are correct, [but the constants may be wrong]

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Wondering what happened to the spoiler tag in previous post, and why I can't edit it to fix.

the spoiler was used incorrectly (no ending spoiler tag)

re second issue, I have disabled editing posts after 10 minutes

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Thanks. I must have deleted the end tag on an edit.

For me, maybe you should disable after zero minutes...

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mgrannis -- will we get the solution?

Or was this a drive-by puzzling?

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