Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Darrell
Posts:
126
Registered:
12/6/04


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


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 poolfilling '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.ryanusa.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 lowermiddle 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 2825 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. 4815253=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 3725=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 4532512=5 like *only* football. 58 like baseball, so 58152512=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 lowerright 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 email to k12math@k12groups.org private email to the k12.ed.math moderator: kemmoderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html



