Subj:
Math Prob. - Buying Four Things At 7-11 (S388b)
From: Anonymous Jr on 7/4/2004
A man went into a 7-11 store
and chose four items. The clerk
calculated the total amount
which came out to $7.11. The cust-
omer thought the price was too
high so he asked the clerk how
he got that total and the clerk
said he multiplied the prices
together to get the total.
The customer asked him to add
the prices together and the clerk
came up with the same total
- $7.11. What were the prices of
the four items the customer
bought?
**The Right Solution**
from Jack:
My first approach was to simply
solve the system of equations,
which of course gives infinite
possibilities. I thought I'd
be able to use substitution
and some "real world" rules to
winnow the results down, but
quickly gave up on that path.
The next approach was to turn
it into more of a logic problem.
Four values, a.bc, d.ef, etc...
with rules about what each
combination gives for its low
digit. I played around with
a.00, d.00, g.hi, j.kl and decided
this was going to be too
complicated.
**The final approach works nicely**.
I'm bothered that there
doesn't seem to be a methodical
way to get to the answer,
but maybe I'm just forgetting
some concepts. Anyway, the
solution:
1) Assume there are no
tricks. That is, the prices are
all positive, and there are
no sub-penny prices - not even
2 for 0.99 or some such combination.
2) Factor the total after
adjusting for the number of items.
Since there are 4 items, each
with a potential value in the
hundredths position this is
7.11 * 100 * 100 * 100 * 100 =
711000000. The factors
are 79, 5, 5, 5, 5, 5, 5, 3, 3, 2,
2, 2, 2, 2, 2 - the 79, 3, 3
from 711 and the 2s and 5s from
the three remaining 100s.
3) There aren't that many
unique combinations of these
factors into four values, and
fewer still that can't be
quickly tossed by inspection.
Trial and error gives:
$3.16 = 79*2*2
$1.50 = 2*3*5*5
$1.25 = 5*5*5
$1.20 = 5*3*2*2*2
---------
$7.11
From:
http://scripts.gophercentral.com/archives/list.asp?a=3?i=DailyTease?rn=577
The items were priced at $1.20, $1.25,
$1.50 and $3.16
which agrees with Jack |