# Word problem (my teacher is crazy)

• May 30th 2008, 12:30 PM
gumi
Word problem (my teacher is crazy)
The following is a well known children's rhyme.

As i was going to St Ives,
I met a man with seven wives;
Every wife had seven sacks;
Every sack had seven cats;
Every cat had seven kits;
Kits,cats, sacks, and wives,
How many were going to St Ives?

Often people answer "one" as the rhyme never indicates that anyone else is actually going to St Ives. However, assuming that the entire group is actually going to St Ives show that the answer to the question is in the rhyme sum of a geometric series, and finds its sum.
• May 30th 2008, 01:07 PM
sean.1986
Quote:

Originally Posted by gumi
The following is a well known children's rhyme.

As i was going to St Ives,
I met a man with seven wives;
Every wife had seven sacks;
Every sack had seven cats;
Every cat had seven kits;
Kits,cats, sacks, and wives,
How many were going to St Ives?

Often people answer "one" as the rhyme never indicates that anyone else is actually going to St Ives. However, assuming that the entire group is actually going to St Ives show that the answer to the question is in the rhyme sum of a geometric series, and finds its sum.

r = 7, a = 1

s5 = (1(1-7^5))/(1-7) = 2801

Plus the man narrating makes it 2802.
• May 30th 2008, 01:30 PM
Soroban
Hello, gumi!

Quote:

As I was going to St Ives,
I met a man with seven wives;
Every wife had seven sacks;
Every sack had seven cats;
Every cat had seven kits;
Kits, cats, sacks, and wives,
How many were going to St Ives?

Assuming that the entire group is actually going to St Ives,
show that the answer to the question is the sum of a geometric series, and finds its sum.

Let's count the items . . .

I met a man with seven wives . . . $1\text{ man, }7\text{ wives}$
Every wife had seven sacks . . . $7^2\text{ sacks}$
Every sack had seven cats . . . $7^3\text{ cats}$
Every cat had seven kits . . . $7^4\text{ kits}$

Then: . $S \;= \;1 + 7 + 7^2 + 7^3 + 7^4 \;=\;2801$

• May 30th 2008, 01:43 PM
sean.1986
Quote:

Originally Posted by Soroban
Hello, gumi!

Let's count the items . . .

I met a man with seven wives . . . $1\text{ man, }7\text{ wives}$
Every wife had seven sacks . . . $7^2\text{ sacks}$
Every sack had seven cats . . . $7^3\text{ cats}$
Every cat had seven kits . . . $7^4\text{ kits}$

Then: . $S \;= \;1 + 7 + 7^2 + 7^3 + 7^4 \;=\;2801$

Wrong. You forgot to include the man who met the man with 7 wives.