My Math Forum System of Equation: Value Problem

 Algebra Pre-Algebra and Basic Algebra Math Forum

 August 2nd, 2018, 12:26 PM #1 Newbie   Joined: May 2018 From: United States Posts: 6 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 >>>>> 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.  August 2nd, 2018, 01:22 PM #2 Global Moderator Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond 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? Thanks from topsquark and Ebba Sen Pai August 2nd, 2018, 03:25 PM #3 Newbie Joined: May 2018 From: United States Posts: 6 Thanks: 0 Math Focus: Algebra Quote:  Originally Posted by greg1313 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. August 2nd, 2018, 03:33 PM #4 Math Team Joined: May 2013 From: The Astral plane Posts: 2,040 Thanks: 814 Math Focus: Wibbly wobbly timey-wimey stuff. Quote:  Originally Posted by Ebba Sen Pai 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  August 2nd, 2018, 05:15 PM #5 Math Team Joined: May 2013 From: The Astral plane Posts: 2,040 Thanks: 814 Math Focus: Wibbly wobbly timey-wimey 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 Thanks from greg1313 and Ebba Sen Pai  August 2nd, 2018, 05:33 PM #6 Global Moderator Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond My mistake. Sorry about that...caution seems to be a habit that eludes me. August 2nd, 2018, 06:44 PM #7 Math Team Joined: May 2013 From: The Astral plane Posts: 2,040 Thanks: 814 Math Focus: Wibbly wobbly timey-wimey stuff. Quote:  Originally Posted by greg1313 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  August 2nd, 2018, 07:42 PM #8 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,950 Thanks: 987 To the corner; both of you: Greg: q + 3 minutes Dan: q - 3 minutes Thanks from topsquark and Ebba Sen Pai  August 2nd, 2018, 08:51 PM #9 Global Moderator Joined: Dec 2006 Posts: 20,270 Thanks: 1958 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. Thanks from greg1313, topsquark and Ebba Sen Pai
 August 3rd, 2018, 01:49 AM #10 Newbie   Joined: May 2018 From: United States Posts: 6 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 Sys-Eq-Val-Problems!

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