SOLUTION: luis chooses a number between 1 and 200. if he divides his number by 10, the remainder is 9. if he divides his number by 8 the remainder is 7 and if he divides his number by 6 the

Question 137143: luis chooses a number between 1 and 200. if he divides his number by 10, the remainder is 9. if he divides his number by 8 the remainder is 7 and if he divides his number by 6 the remainder is 5. what is the number luis chose?
is there any way to solve this question besids guess and check
thanks for any help
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
luis chooses a number between 1 and 200. if he divides his number by 10, the remainder is 9. if he divides his number by 8 the remainder is 7 and if he divides his number by 6 the remainder is 5. what is the number luis chose?
---------------
Let the number be y where 1 -----------------
EQUATIONS:
y = 10m + 9 where m is an integer.
y = 8n + 7 where n is an integer
--------------------
10m+9 = 8n+7
10m-8n = -2
---------------
Examine integral multiples of 10 and integral multiples of 8
till you find a difference of -2.
-----------
10m = 30 8n=32
m=3 nd n=4
-----------------
Therefore y = 10m+9 = 10*3 +9 = 39
Checking: y = 8n+7 = 8*4 + 7 = 39
=========================
Luis chose the number 39
===============================
Cheers,
Stan H.
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