how many of each coin / present ages / travelling for 9 hrs

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caitlynbby007

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Sep 19, 2008
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1. In a child's bank, there is a collection of nickels, dimes, and quarters which amounts to $4.15. There are 4 times as many dimes as nickels, and there are 3 less quarters than nickels. How many coins of each kind are there?

2. Ray is 20 years older than Bill. Five years ago, Ray was 5 times as old as Bill was then. Find the present age of both Ray and Bill.

3. How far can a man drive out in the country at an average rate of 50 mph and return over the same road at the average rate of 40 mph if he travels a total of 9 hrs?

Help would be GREATLY appreciated. I'm about to spaz out here. :cry:
 
It never hurts to try something ... anything ...

Hello there:

The way it works at these help boards is that you show us what you're thinking about a particular exercise, and you show us any work that you've been able to do so far. It would also be great if you could say something about why you're stuck.

Nobody here really has any idea of why you're stuck or what you know until after we see what you're doing.

I'll start with some basics on the first exercise.

Since they tell you about dimes and quarters in terms of nickels, it makes sense to choose a variable name to represent the unknown number of nickels. By doing this, we can then write expressions for both the unknown number of dimes and the unknown number of quarters.

N = the number of nickels

Since there are three less quarters than nickels, can you see why the following is true?

N - 3 = the number of quarters

For the dimes, we're told that the number dimes is four times the number of nickels.

4N = the number of dimes.

Is this enough information for you to get going on exercise 1?

Please show your work here if you need more help on exercise 1.

Please tell us what you think about the remaining exercises, too.

Cheers,

~ Mark :)
 
Re: Word problems that deal with d=rt and others

You don't say whether to solve using one variable or more than one. I'll assume one.

............number of coins......value of one.........Total value
nickels.....___x___.................5...................._____
dimes......_______................10...................._____
quarters..._______................25...................._____
Total......_______......................................._415_

Now, fill in the blanks in terms of x and build your equation using the right hand column. The heading should read "number of coins times the value of each equals the total value. I have set this up in cents rather than dollars to avoid the decimal points.
 
Re: Word problems that deal with d=rt and others

Okay, well, for the first problem I tried this:

n/4=d n-3=q (so that I have them all in like terms)

4.15=.05n+.10d+.25q
4.15=.05n+.10(n/4)+.25(n-3)
4.15=.05n+1/40n+.25n-.75
4.90=.325n
n=15.077

^^I don't understand where I went wrong.


For the second problem I tried:

r=20+b
b+(20+b)-5=(b+5b)
2b+15=6b
15=4b
? That gives me some crazy decimal that can't be right..
I don't know how to set up the problems.

Thanks Mark.




Loren, It is solving for one variable.
Sorry about the confusion, I'm new to this.
I'm about to try your method.
I think I understand what you mean.
Thanks.
 
Re: Word problems that deal with d=rt and others

caitlynbby007 said:
Okay, well, for the first problem I tried this:

n/4=d ? This is not correct.

It would ONLY be correct if the exercise told us that "there are one-fourth as many dimes as nickels".

You need to use the expression for dimes that I posted earlier.

d = 4*n

4.15=.05n+.10(4*n)+.25(n-3)

Try again with this corrected equation ...
Click to expand...
 
Re: Word problems that deal with d=rt and others

caitlynbby007 said:
For the second problem I tried:

r=20+b
b+(20+b)-5=(b+5b)
2b+15=6b
15=4b
Click to expand...

Your first line above is great.

B = Bob's age now

Then Rob's age now is R = B + 20

Okay, now we need to think about their age's five years ago.

B - 5 is Bob's age five years ago.

R - 5 is Rob's age five years ago.

The exercies tells us that five years ago, Rob's age was 5 times Bob's.

R - 5 = 5(B - 5)

Substitute the expression that you wrote for Rob's age now into this equation and solve for B.

Cheers,

~ Mark :)
 
Re: Word problems that deal with d=rt and others

Wow, you're like a miracle worker. haha

Okay, last one and I promise I'll leave you alone, for now at least. :wink:

How far can a man drive out in the country at an average rate of 50 mph and return over the same road at the average rate of 40 mph if he travels a total of 9 hrs?



Thanks again!
 
Re: Word problems that deal with d=rt and others

caitlynbby007 said:
How far can a man drive out in the country at an average rate of 50 mph and return over the same road at the average rate of 40 mph if he travels a total of 9 hrs?
Click to expand...

You know that distance is equal to the product of rate and time.

d = r * t

When working exercises with this formula, it's often necessary to rearrange it into a formula for time OR a formula for rate.

t = d/r

r = d/t

In your exercise, we need to find d.

They give us the total driving time of 9 hours.

Since the rates are give in terms of miles/hours, we know that the formula for time (d/r) is in hours.

How many hours does it take to drive distance d at 50mph?

Use the formula for time.

t = d/50

In other words, the expression d/50 represents a number of hours.

Write an expresssion for the number of hours it takes driving back at 40mph.

Add these two expressions for time to get 9, and solve the resulting equation for d.

Cheers,

~ Mark :)
 
Re: Word problems that deal with d=rt and others

caitlynbby007 said:
How far can a man drive out in the country at an average rate of 50 mph and return over the same road at the average rate of 40 mph if he travels a total of 9 hrs?
Click to expand...
Sometimes a picture is worth a 1000 words:
@50..........d.................> h (hours)
(9-h)<........d................@40

Now easy to see that 50h = 40(9-h); kapish?
 
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