February 22nd, 2018, 08:31 AM  #1 
Newbie Joined: Feb 2018 From: dont share Posts: 4 Thanks: 0  Algebra Problem Solving Question
I need help on this algebra word problem as I don't know how to work out the number of stamps and I don't know how to approach this question. Thank You and help is appreciated. Question: jjjjjjj.jpg Last edited by skipjack; February 22nd, 2018 at 02:24 PM. 
February 22nd, 2018, 08:49 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 924 Thanks: 369 
The first step is to assign letters to represent the numbers that may be relevant but that you do not yet know. What letters have you assigned to what?

February 22nd, 2018, 09:03 AM  #3 
Newbie Joined: Feb 2018 From: dont share Posts: 4 Thanks: 0 
a = alex b = bryan c = calvin I have found that $\displaystyle a = \frac{b+c+78}{2}$ and that $\displaystyle b = \frac{(b+c+78/2)+ c +78}{3}$ and that c can be found by adding a and b and 78, but I don't know how I could do that as the equations look complicated and after many attempts I still can't try to solve it. Last edited by skipjack; February 22nd, 2018 at 02:27 PM. 
February 22nd, 2018, 09:29 AM  #4 
Senior Member Joined: May 2016 From: USA Posts: 924 Thanks: 369  Great. Always the way to start. You have three unknowns. Therefore you need three numeric clues involving the unknown numbers. Using your letters, write down what you know about numbers that pertain to your unknowns. The second sentence gives you a clue. How do you write it down in algebraic notation? The third sentence gives you another clue. How do you write it down in algebraic notation? The fourth sentence gives you one more clue. How do you write it down in algebraic notation? You now have a pure algebra problem. Do you know what to do next? Last edited by skipjack; February 22nd, 2018 at 03:08 PM. 
February 22nd, 2018, 09:33 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1017 Math Focus: Elementary mathematics and beyond 
One of nstar348's previous posts was automoderated and therefore hidden. I've approved it so it is now visible.

February 22nd, 2018, 09:38 AM  #6 
Newbie Joined: Feb 2018 From: dont share Posts: 4 Thanks: 0 
The reply I made before you replied with my workings out  that is what I think I have to do next, but I don't know after.
Last edited by skipjack; February 22nd, 2018 at 02:29 PM. 
February 22nd, 2018, 09:53 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1017 Math Focus: Elementary mathematics and beyond 
$\displaystyle D = 78$ $\displaystyle A = \frac{B + C + D}{2}\Rightarrow2A=B+C+78\Rightarrow2ABC=78$ $\displaystyle B = \frac{A + C + D}{3}\Rightarrow3B=A+C+78\RightarrowA+3BC=78$ $\displaystyle C = \frac{A + B + D}{4}\Rightarrow4C=A+B+78\RightarrowAB+4C=78$ The RHS is a system of 3 equations in 3 variables but there is a shortcut: $$AB+4C=78\implies A+B=4C78$$ So all you have to do is find $C$ and substitute that value into the equation above. Can you proceed? 
February 22nd, 2018, 10:05 AM  #8 
Newbie Joined: Feb 2018 From: dont share Posts: 4 Thanks: 0 
I'm a bit confused at how I could work out c when I don't have a number value for a and b.
Last edited by skipjack; February 22nd, 2018 at 02:31 PM. 
February 22nd, 2018, 10:16 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1017 Math Focus: Elementary mathematics and beyond 
The problem asks you to find the number of stamps that Alex and Bryan have altogether. We have arrived at the equation A + B= 4C  78 so, by finding a value for C (which is 72) we write A + B = 4 * 72  78 = 210, so Alex and Bryan have a total of 210 stamps. Can you find C using the given information? 
February 22nd, 2018, 03:09 PM  #10 
Global Moderator Joined: Dec 2006 Posts: 18,719 Thanks: 1536 
As 8a + 9b + 20c = 4(b + c + 78) + 3(a + c + 78) + 5(a + b + 78) = 8a + 9b + 7c + 12(78), 13c = 12(78), and so c = 72. 

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