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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.
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
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.
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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