word problem: "If q represents the number of quarters..."

[agapela]

Hi, I am studying for a Math Competency Exam. There is one algebra problem in my study guide that I can't figure out:

A collection of coins consists of nickels, dimes, and quarters. There are 3 more dimes than quarters and 2 more nickels than quarters. All of the coins together are worth $2.00. If q represents the number of quarters, which of the following equations represents the situation?

Correct Answer: 25q + 10q + 30 + 5q + 10 = 200

Could someone walk me through it?

 

[ksdhart]

First off, let's assign some variables to our terms. I'll use n for nickels, d for dimes, and q for quarters. A nickel is worth 5 cents, a dime worth 10, and a quarter worth 25. And the total amount of money we have is $2.00, or 200 cents. So, our initial equation is:

5n + 10d + 25q = 200

Then we're told that there are 3 more dimes than quarters. Based on this information, can you then set up an equation for d in terms of q? And the same applies to the nickels, except there are 2 more nickels than quarters. After you have equations for d and n, simply substitute those into the main equation. Then you'll have something like this:

5 * (n in terms of q) + 10 * (d in terms of q) + 25q = 200

Although the problem leaves the answer in the above form, you can go another step and combine your q terms then solve for q, to find the exact number of each coin. I'd strongly recommend doing this, as practice for other problems which may ask you to do just that.

 

[Dale10101]

?

Hi, I am studying for a Math Competency Exam. There is one algebra problem in my study guide that I can't figure out:

A collection of coins consists of nickels, dimes, and quarters. There are 3 more dimes than quarters and 2 more nickels than quarters. All of the coins together are worth $2.00. If q represents the number of quarters, which of the following equations represents the situation?

Correct Answer: 25q + 10q + 30 + 5q + 10 = 200

Could someone walk me through it?

Something seems wrong here. The problem suggests that if I have 1 quarter in my pocket then then I must have 3 more (not times) dimes then the one quarter in my pocket, i.e. 4 dimes, and by the same token, 2 more nickels in my pocket then the one quarter, or three nickels. In toto if I have a single quarter in my pocket then I must also have 25 cents + 4(10 cents) +3(5 cents) = 80 cents in my pocket. In that case if I have two quarters in my pocket then I must have a $1.60 in my pocket, and again, 3 quarters, $2.40, i.e you cannot have a total of $2.00 under the conditions stated.

Of course $200.00 would work ($200/.8 = 250 units of 1 quarter, 4 dimes, 3 nickels = 250 Q, 1000 D, 750 N), but then with that much change in ones pocket ones pants would fall done and that must be an error, so disregard this walking backwards off the cuff analysis which at best might give you a cryptic clue to the equation you seek. Listen to KD and St Denis, they know the way to heaven . :roll:

 

[ksdhart]

Dale, your reasoning for why this problem has no answer is flawed. Your total for when there is one quarter (i.e. q = 1) is correct, but it goes astray from there. Your solution assumes you have x discrete units of 1 quarter, 4 dimes, and 3 nickels. But that's not what the problem says. From the text of the problem we're given d = q + 3 and n = q + 2. Let's make a table and see what happens:

1 Quarter, 4 Dimes, 3 Nickels: 80 cents
2 Quarters, 5 Dimes, 4 Nickels: 120 cents
3 Quarters, 6 Dimes, 5 Nickels: 160 cents
and so on...

Hope that helps your confusion

 

[Dale10101]

Danke

Dale, your reasoning for why this problem has no answer is flawed. Your total for when there is one quarter (i.e. q = 1) is correct, but it goes astray from there. Your solution assumes you have x discrete units of 1 quarter, 4 dimes, and 3 nickels. But that's not what the problem says. From the text of the problem we're given d = q + 3 and n = q + 2. Let's make a table and see what happens:

1 Quarter, 4 Dimes, 3 Nickels: 80 cents
2 Quarters, 5 Dimes, 4 Nickels: 120 cents
3 Quarters, 6 Dimes, 5 Nickels: 160 cents
and so on...

Hope that helps your confusion

Thanks, I will think about this until it is clear. Glad for the correction.

 

[Ishuda]

Something seems wrong here. The problem suggests that if I have 1 quarter in my pocket then then I must have 3 more (not times) dimes then the one quarter in my pocket, i.e. 4 dimes, and by the same token, 2 more nickels in my pocket then the one quarter, or three nickels. In toto if I have a single quarter in my pocket then I must also have 25 cents + 4(10 cents) +3(5 cents) = 80 cents in my pocket. In that case if I have two quarters in my pocket then I must have a $1.60 in my pocket, and again, 3 quarters, $2.40, i.e you cannot have a total of $2.00 under the conditions stated.

Of course $200.00 would work ($200/.8 = 250 units of 1 quarter, 4 dimes, 3 nickels = 250 Q, 1000 D, 750 N), but then with that much change in ones pocket ones pants would fall done and that must be an error, so disregard this walking backwards off the cuff analysis which at best might give you a cryptic clue to the equation you seek. Listen to KD and St Denis, they know the way to heaven . :roll:

Dale,
You are multiplying if you do it that way, not adding. The way you have it if you have 2 quarters, then you have it as
2 [ 25 cents + 4(10 cents) +3(5 cents) ] = 2(25 cents) + 8(10 cents) +6(5 cents) = $1.60
But the problem is, for two quarters,
2(25 cents) + (2+3)(10 cents) +(2+2)(5 cents) = $1.30

 

[Dale10101]

OK

Dale,
You are multiplying if you do it that way, not adding. The way you have it if you have 2 quarters, then you have it as
2 [ 25 cents + 4(10 cents) +3(5 cents) ] = 2(25 cents) + 8(10 cents) +6(5 cents) = $1.60
But the problem is, for two quarters,
2(25 cents) + (2+3)(10 cents) +(2+2)(5 cents) = $1.30

I see what is going on, my interpretation of what is being asked is different and I think corresponds to what I wrote ... there is a collection of coins, if you put in a quarter then you must put in 3 more coins then that in dimes, and two more coins then that in nickels. If the total is $200.00, how many quarters, dimes and nickels were added to create the collection.

I can see that your interpretation is undoubtedly what the author meant. Ah well.