Math Forum Discussions

Darrell

Posts: 126
Registered: 12/6/04

Re: Word Problem help
Posted: Apr 17, 2004 12:34 PM

Plain Text

Since you haven't shown any work on these, I can't know exactly what you're
doing wrong but I will try to get you started in the right direction, and in
one problem I went ahead and worked it completely. Please don't just copy
the answer. If you do you are only hurting yourself because no one is going
to just hand you the answer come test time. Be sure to double check
everything (I wrote this all very rapidly, I have a ball game in an hour).

"jacqueline" <jacquelinem59@hotmail.com> wrote in message
news://3bn180pn63c4gk7rn3mossq27vemtqnfkv@4ax.com...
> i ahve a few word problems that are getting to me.... my sister had
> them and she doesnt remember the answers they were from her class. if
> you could help it would be great
> here are a few of teh questions....
> 1. 2 pumps can fill a pool in 4 and 5 hrs respectively.

...so the slower one takes 1 hour longer to fill the same pool, if it were
filling it alone.

> at noon the
> slower one is turned on and at 1"00 the other is started.
> at what time
> will the pool be filled.

Since the faster pump fills the pool (alone) in 4 hours, it fills 1/4 the
pool in 1 hour, i.e. completes 1/4 of the entire pool-filling 'job'. The
slower pump fills 1/5 the pool in 1 hour, i.e. takes one hour to complete
1/5 of the same job.

The parts of the jobs done by each pump, must add to "1" job.

part done by fast pump + part done by slow pump = 1

The part done by each pump is the rate per hour at which it pumps (1/4 and
1/5 respectively) times the #of hours pumped. The total #of hours pumped is
what you're looking for, so assign it a variable (why not h for hours).
This means...

1/4(h) + (1/5)h = 1

> 2. how many 6 digits palindromic numbers are there?

...meaning its the same number written forward and backward, e.g. 100001.
It's basically a 'counting' problem, not at all dissimilar (fundamentally)
to another recent counting problem asked. For the first three digits, just
count up the possible ways they can each individually turn out. Assuming no
leading 0's are allowed, this means the first digit has 1 less way it can
turn out, than the second and third digits have. By Multiplication
Principle:

# of three digit numbers (assume no leading 0's) is:

# of ways to choose the 1st digit
times
# of ways to choose the 2nd digit
times
# of ways to choose the 3rd digit

Since the last three digits are the mirror image of the first three, the
number of them are the same (just in a different order) so just double this
result. If you allow leading (thus trailing) 0's then just make the
appropriate correction in the #of ways the first digit can be chosen.

> 3. of 75 students surveyed: 48 like basketball,45 like footbal,58 like
> baseball,28 like basket and foot,37 like foot and base, 40 like basket
> and base,and 25 like all 3
> how many like only baseball, and how many dont like any?

This is a good problem for a Venn diagram. These can be a little tricky to
explain without actually showing you a diagram, so I have made one and put
it at the link below. I'll explain how I got the numbers, so hopefully you
can read the explanation while looking at the diagram (print one or both, or
at least open both in different windows side by side.)

I have worked this out, but don't just copy the answer and turn it in
without trying to understand it. That won't help you come test time.

http://aah.ryan-usa.com/venndiagram.gif

If you understand a little about set terminology, you know the 'universe' is
75. Since the entire box represents this universal set, all numbers within
the box must sum to 75.

Each of the three circles within the box represents a sport. They are
subsets of the 75. The leftmost circle is basketball, the rightmost is
baseball, and the lower-middle circle is football. Start by simply drawing
three circles in a box. Don't worry about the numbers yet, just make sure
they overlap in the correct fashion as shown.

The 'overlapping' regions represents common ground, i.e. intersections
between sets. The particular intersection they represent depends on which
particular overlapping section you're looking at. As you see, there is a
region where basketball and football overlap, a region where football and
baseball overlap, a region where basketball and baseball overlap, and yet
another region where all three overlap.

Start with the region where all three overlap. Since 25 like all three,
place 25 here.

See the little section just above that one, where *only* basketball and
baseball overlap? 40 like basketball and baseball, but don't count the
number that like all three when determining what number goes here. It's
important to realize that the section we are currently referring to is the
number of people that like basketball and baseball, but do *not* like all
three. The ones liking all three are already accounted for. Since 40 like
basketball and baseball, and 25 of them are already accounted for (by way of
liking all three), then the number that goes here is the difference between
40 and 25 which is 15.

You now have enough numbers to complete the basketball circle. There is but
one remaining section, representing the people that like *only* basketball.
Realize this is a different set from the people that like basketball (since
some like other sports, too). to get the number that goes here, simply
subtract the three other numbers in the basketball circle, from 48 (you were
told 48 like basketball in all). That's where that 5 comes from.

Next, look at the region where basketball and football overlap and proceed
in similar fashion. You are told 28 like both basketball and football.
Again, 25 of them are already accounted for, so in the section where *only*
basketball and football overlap, you place 28-25 which is 3.

You now have enough information to fill in the remaining section of the
basketball circle, representing those that like *only* basketball. Since 48
like basketball, then subtract the other numbers in the entire basketball
circle. 48-15-25-3=5.

next, consider the section where football and baseball overlap. You are
told 37 like football and baseball, and again 25 of these are already
accounted for. So 37-25=12 goes in the blank part of that section where
*only* football and baseball overlap.

You now have enough information to fill in the remaining section. You are
told 45 like football, so 45-3-25-12=5 like *only* football. 58 like
baseball, so 58-15-25-12=6 like *only* baseball.

Finally, since the entire box must sum to 75, the number that don't like
*any* is 75-(all other numbers), and is placed inside the box but outside
the circles, usually in the lower-right corner. that's where the 4 comes
from. As you see, this allows for easy answering of just about any question
concerning these people and the these sports, not just the two questions
asked. For ex. you can easily see that number of people that like
basketball and football, but do *not* like baseball, is 3, or that the
number of people liking *just* football is 5, etc.

--
Darrell

--
submissions: post to k12.ed.math or e-mail to k12math@k12groups.org
private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org
newsgroup website: http://www.thinkspot.net/k12math/
newsgroup charter: http://www.thinkspot.net/k12math/charter.html