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Question 479955: Michael is thinking of two 2-digits numbers X and Y. X and Y shares the same two digits and the ratio of X to Y is 4/7. She halves the value of X and reduced the value of Y to 1/3 its original value. Next, she subtracts 3 from Y. Both X and Y has the same value now. What was the original numbers X and Y?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Michael is thinking of two 2-digits numbers X and Y. X and Y shares the same two digits and the ratio of X to Y is 4/7. She halves the value of X and reduced the value of Y to 1/3 its original value. Next, she subtracts 3 from Y. Both X and Y has the same value now. What was the original numbers X and Y?
be
Let X be 10t+u
Y= 10u+t
(10t+u)/(10u+t)=4/7
7(10t+u)=4(10u+t)
70t+7u=40u+4t
66t-33u=0
2t-u=0..............1
1/2(10t+u) = ((10u+t)-3)/3
3(10t+u)=2((10u+t)-3)
30t+3u=20u+2t-6
32t-17u=-6...................2
but u =2t
substitute u in (2)
32t-17*2t=-6
32t-34t=-6
-2t=-6
/-2
t=3
Therefore u=6
The numbers are 36 & 63
CHECK
36/63 = 4/7
m.ananth@hotmail.ca
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