# algebra

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: If Bobby fives Jane three pens, they have the same number of pens. But if Jane gives Bobby three pens,he will have three times as many pens. How many pens does each student have?

• algebra -

number of pens for Bob --- x
number of pens for Jane --- y

case1: Bob gives 3 pens to Jane
Bob has x-3
Jane has y+3
so x-3 = y+3
x-y = 6

case2: Jane gives 3 pens
Bob has x+3
Jane has y-3
x+3 = 3(y-3)
x+3 = 3y - 9
x - 3y = -12

subtract the two equations
2y = 18
y = 9
sub into 1st equation:
x-9 = 6
x = 15

Bob now has 15 and Jane has 9
after 1st transfer, bob has 12 and Jane has 12, good!
afer 2nd transfer, Bob has 18 and Jane has 6
does he have 3 times what she has? YES!
all is good!

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