August 2nd, 2018, 11:26 AM  #1 
Newbie Joined: May 2018 From: United States Posts: 5 Thanks: 0 Math Focus: Algebra  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 >>>>> numbervalue  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. 
August 2nd, 2018, 12:22 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond 
Hi Ebba Sen Pai; I've approved your post. Let h be halfdollars and q be quarters: h = q + 3 25q + 50(q + 3) = 375 Can you make sense out of that? Can you continue from there? 
August 2nd, 2018, 02:25 PM  #3 
Newbie Joined: May 2018 From: United States Posts: 5 Thanks: 0 Math Focus: Algebra  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.

August 2nd, 2018, 02:33 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 749 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
25q + 50(q + 3) = 375 25q + 50q + 50 * 3 = 375 (25 + 50)q + 150 = 375 75q + 150 = 375 Can you finish? Dan  
August 2nd, 2018, 04:15 PM  #5 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 749 Math Focus: Wibbly wobbly timeywimey stuff. 
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 
August 2nd, 2018, 04:33 PM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond 
My mistake. Sorry about that...caution seems to be a habit that eludes me.

August 2nd, 2018, 05:44 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,852 Thanks: 749 Math Focus: Wibbly wobbly timeywimey stuff.  
August 2nd, 2018, 06:42 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,902 Thanks: 882 
To the corner; both of you: Greg: q + 3 minutes Dan: q  3 minutes 
August 2nd, 2018, 07:51 PM  #9 
Global Moderator Joined: Dec 2006 Posts: 19,285 Thanks: 1681 
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.

August 3rd, 2018, 12:49 AM  #10 
Newbie Joined: May 2018 From: United States Posts: 5 Thanks: 0 Math Focus: Algebra 
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 SysEqValProblems! 

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