SOLUTION: Hi Leo and issac had 95 balls together. Leo gave away 3 more than issac. Issac was left with 5 fewer than the balls he gave away. Leo had 2 more balls left than issac. How many di

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Question 1203379: Hi
Leo and issac had 95 balls together. Leo gave away 3 more than issac. Issac was left with 5 fewer than the balls he gave away. Leo had 2 more balls left than issac. How many did Leo give away.
Thanks


Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
           INITIAL    GAVE AWAY
Leo          e         e-x-3
Isaac        i         i-x
TOTAL        95


system%28i-x=x-5%2Ce-x-3=i-x%2B2%2Ce%2Bi=95%29

--
system%28i-2x=-5%2Ce-i=5%2Ce%2Bi=95%29

i=2x-5
-
system%28e-%282x-5%29=5%2Ce%2B2x-5=95%29

system%28e-2x%2B5=5%2Ce%2B2x=100%29

system%28e=2x%2Ce%2B2x=100%29

substitute for e.
2x%2B2x=100
x=25--------------------------

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
(a) Leo and issac had 95 balls together.
(b) Leo gave away 3 more than issac.
(c) Issac was left with 5 fewer than the balls he gave away.
(d) Leo had 2 more balls left than issac.
How many did Leo give away.
~~~~~~~~~~~~~~~ 

x = Leo had initially
y = Issac had initially
z = Leo gave away

From (a), we have this equation   x + y = 95.             (1)

From (b), Issac gave away (z-3).

From (c), we have this equation   y - (z-3) = ((z-3)-5),  or   y - 2z = -11   (2)

From (d), we have this equation   x - z = y - (z-3) + 2,  or   x -  y =   5   (3)



Thus, we have this system of equations

    x +  y      =  95    (1)

         y - 2z = -11    (2)

    x -  y      =   5    (3)


Add equations (1) and (3).  Get  2x = 100,  x = 100/2 = 50.    (Leo had initially)


Then from (1),  y = 95 - x = 95 - 50 = 45.                     (Issac had initially)


Then from (2),  2z = y + 11 = 45 + 11 = 56,  z = 56/2 = 28.    (Leo gave away)


ANSWER.  Leo gave away 28 balls.


CHECK.  Issac gave away 28-3 = 25.

        Issac was left with 45 - 25 = 20.

        Leo was left with 50 - 28 = 22.

        Leo left - Issac left = 22 - 20 = 2   (correct).

Solved.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


With a little bit of analysis, the problem can be solved using a single variable....

Let x = number Isaac gave away [the number the question asks for]

Then x-5 = number Isaac had left [he was left with 5 fewer than he gave away]

And x+3 = number Leo gave away [3 more than Isaac gave away]

And finally, 95-(x+(x-5)+(x+3)) = 97-3x = number Leo had left [the total number was 95]

Leo had left 2 more than Isaac:

97-3x=%28x-5%29%2B2
4x=100
x=25

ANSWER: Isaac gave away 25 balls

Solving the problem using a system of 3 equations with 3 variables, as both of the other tutors did, is good algebra; however, the work required to actually solve the problem is very often much easier if you take some time to analyze the problem to find how to set it up using a single variable.