SOLUTION: Hi Ken and Ivan had some sweets. After ken gave away 5/7 of his sweets, he had 2/3 as many as ivan. ivan then gave away 120 sweets and he had 1/4 as many sweets as ken. How many

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Question 1051843: Hi
Ken and Ivan had some sweets. After ken gave away 5/7 of his sweets, he had 2/3 as many as ivan.
ivan then gave away 120 sweets and he had 1/4 as many sweets as ken. How many did each have at first.
thanks
Found 3 solutions by josgarithmetic, MathTherapy, advanced_Learner:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
MISTAKE FOUND*

Ken has x sweets.
Ivan has y sweets.



ken gave away 5/7 of his sweets, he had 2/3 as many as ivan.
%282%2F7%29x=%282%2F3%29y


ivan then gave away 120 sweets and he had 1/4 as many sweets as ken.
y-120=%281%2F4%29%282%2F7%29x


Simplify each equation.
-
x=%287%2F2%29%282%2F3%29y
x=%287%2F3%29y
-
* y-120=%287%2F2%29x-------------MISTAKE HERE! Ruins the rest of the work.
y=%287%2F2%29x%2B120
-
Substitute for x.
y=%287%2F2%29%287%2F3%29y%2B120
Solve this for y.
y=%2849%2F6%29y%2B120
6y=49y%2B6%2A120
0=43y%2B720---------------This makes no sense. y would be negative.


* MISTAKE IDENTIFIED; solution process not yet corrected

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Ken and Ivan had some sweets. After ken gave away 5/7 of his sweets, he had 2/3 as many as ivan.
ivan then gave away 120 sweets and he had 1/4 as many sweets as ken. How many did each have at first.
thanks
At first,

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
Ken and Ivan had some sweets. After ken gave away 5/7 of his sweets, he had 2/3 as many as ivan.
ivan then gave away 120 sweets and he had 1/4 as many sweets as ken. How many did each have at first.
thanks

%282%2F7%29%2Ak=%282%2F3%2AI%29
%28I-120%29=%281%2F4%29%2A%282%2F7%29k
first part
%28k%29=%287%2F2%29%282%2F3%2AI%29
k=%287%2F3%2AI%29
3k=%287%2AI%29
second part
%28I-120%29=%281%2F14%29k%29
%2814I-1680%29=k%29
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++3%5Ck+%2B+-7%5CI+=+0%2C%0D%0A++++-1%5Ck+%2B+14%5CI+=+1680+%29%0D%0A++

Any system of equations:


has solution

or



(k=336, I=144}