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Beth and Alex have 155p between them.Beth has 15p more than Alex.Beth have x p and Alex...

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sera72 | Student, Grade 9 | eNotes Newbie

Posted November 25, 2009 at 7:55 PM via web

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Beth and Alex have 155p between them.Beth has 15p more than Alex.Beth have x p and Alex have y p. How do I formulate a simulteneous equation

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neela | High School Teacher | Valedictorian

Posted November 25, 2009 at 8:14 PM (Answer #1)

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From the data, the p's with Beth and Alex are xp and yp and their total is 155p. This is formulated as:

xp+yp = 155p .............(1)

Beth's xp is 15p more than Alex's yp. So,

xp-yp = 15P.................(2)

The two equations at (1) and (2) are the simultaneous equations which could now be solved for x and y and their values  could be expressed in terms of  p's.

 

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted November 25, 2009 at 10:58 PM (Answer #2)

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Simultaneous equations are equations that have these following characterisitics:

  • They have multiple variables
  • The variables must be solved for simultaneously.

In the situation you have provided your variables are x (Beth) and y (Alex).  Think about what you know and what equations you can make:

Between them they have 155p.  You can express this as x + y = 155  because Beth's money plus Alex's is 155p.

But you also know how to compare the amounts they have.  Beth has 15p more so x = y + 15 because Beth's amount of money (x) is Alex's (y) plus 15.

So your equations are

x + y = 155

and

x = y + 15

So, what you're trying to do is ask yourself "what do I know about the relationships between the variables?"  Once you figure that out, you ask "how do I express that relationship mathematically?"

I hope that helps you understand the process of getting the right answer.

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amarang9 | College Teacher | (Level 1) Educator Emeritus

Posted November 26, 2009 at 2:48 AM (Answer #3)

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I'm not sure this is a 'simultaneous equation' but this is how i'd solve it.

'p' is just the unit, not a variable, so ignore 'p' for now.

Beth and Alex have 155 between them.

Beth has 15 more than Alex. Beth's amount is represented by x and Alex's amount is represented by y. Since Beth has 15 more than Alex, instead of using x for Beth, use (y+15). Now, Alex is y and Beth is (y+15).

The first equation would be: x + y = 155.

Substituting (y+15) for Beth's x, the new equation is:

y + (y+15)  = 155

Solve for y: 2y + 15 = 155

2y = 140

y = 70

Beth is x, or (y +15), so x = (70+15)

x = 85

Then you can add 'p'. Alex has 70p and Beth has 85p giving 155p in total.

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