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August 2nd, 2018, 11:26 AM   #1
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System of Equation: Value Problem

I have just taken a test and know that I got this problem wrong (I copied it to my scratch paper to ask here). My book provided me many useful examples for comparable questions, but not one quite like this (checked twice).
I am wondering what the solution is for this problem, as I sadly have no idea.
Problem:
$3.75 is made up of quarters and half dollars. If the number of quarters exceeds the number of half dollars by 3, how many coins of each denomination are there?


I know it is helpful to build a table such as

>>>>> number|value | total
|-------------------------------------
item 1 | q+3 | 25 |>> 25q+75
item 2 | h >> | 50 | >> 50h
total | ? |>>>>>>>>>| 375
|
-------------------------------------
(using ">>>>" above to try to keep format, for some reason spaces dissapear when actually posting, so table loses proportions)

but either I am inputting the wrong data into the table above, or I do not know how to execute the next steps after the two equations that can be taken from the above data have been built:

q+3=h
25q+75+50h=375

Where have I gone wrong, or what would be the appropriate next steps?
My humblest thanks to anyone gracious enough to assist me on this peculiar question.
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August 2nd, 2018, 12:22 PM   #2
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Hi Ebba Sen Pai; I've approved your post.

Let h be half-dollars and q be quarters:

h = q + 3

25q + 50(q + 3) = 375

Can you make sense out of that? Can you continue from there?
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August 2nd, 2018, 02:25 PM   #3
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Quote:
Originally Posted by greg1313 View Post
Hi Ebba Sen Pai; I've approved your post.

Let h be half-dollars and q be quarters:

h = q + 3

25q + 50(q + 3) = 375

Can you make sense out of that? Can you continue from there?
That helps a great deal to show where I have gone wrong. Sadly I am now finding that I am not sure of the next steps. My deepest apologies as I was initially sure your provided steps would be all I needed. If you or anyone else could provide the following steps I would be humbled and will study them until I know exactly how to replicate them for future problems.
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August 2nd, 2018, 02:33 PM   #4
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Quote:
Originally Posted by Ebba Sen Pai View Post
That helps a great deal to show where I have gone wrong. Sadly I am now finding that I am not sure of the next steps. My deepest apologies as I was initially sure your provided steps would be all I needed. If you or anyone else could provide the following steps I would be humbled and will study them until I know exactly how to replicate them for future problems.
Always, always ask for what you need. You don't need to apologize for that.

25q + 50(q + 3) = 375

25q + 50q + 50 * 3 = 375

(25 + 50)q + 150 = 375

75q + 150 = 375

Can you finish?

-Dan
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August 2nd, 2018, 04:15 PM   #5
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Denis tells me (correctly) that q = h + 3 so h = q - 3, which makes the equation
25q + 50h = 375

25q + 50(q - 3) = 375

25g + 50g - 50 * 3 = 375

(25 + 50)g - 150 = 375

75g - 150 = 375

-Dan
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August 2nd, 2018, 04:33 PM   #6
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My mistake. Sorry about that...caution seems to be a habit that eludes me.
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August 2nd, 2018, 05:44 PM   #7
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Quote:
Originally Posted by greg1313 View Post
My mistake. Sorry about that...caution seems to be a habit that eludes me.
It happens. I am just as responsible since I should have checked it on my own before accepting your result. So to Ebba Sen Pai I also apologize.

-Dan
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August 2nd, 2018, 06:42 PM   #8
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To the corner; both of you:
Greg: q + 3 minutes
Dan: q - 3 minutes
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August 2nd, 2018, 07:51 PM   #9
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Ignoring three of the quarters, there are equal numbers of quarters and half dollars, worth \$3 in total, so there are 4 of each. Hence there are originally 4 half dollars and 7 quarters.
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August 3rd, 2018, 12:49 AM   #10
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I wanted thank everyone for the fantastic responses. I had struggled with understanding the steps involved here and couldn't piece together the specifics required to fully grasp why I was so off base on my own. Thanks to all of your glorious responses (and modifications) I can see exactly what went so wrong in terms of my solving this problem and feel incredibly comfortable with this type of problem now! I know it's cliche, but now... "It just makes sense."
My book didn't go into enough helpful detail about the particulars involved (for me), but I now feel liberated from the dragon of Sys-Eq-Val-Problems!
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