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?
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Let the number be y where 1<y<200.
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EQUATIONS:
y = 10m + 9 where m is an integer.
y = 8n + 7 where n is an integer
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10m+9 = 8n+7
10m-8n = -2
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Examine integral multiples of 10 and integral multiples of 8
till you find a difference of -2.
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10m = 30 8n=32
m=3 nd n=4
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Therefore y = 10m+9 = 10*3 +9 = 39
Checking: y = 8n+7 = 8*4 + 7 = 39
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Luis chose the number 39
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Cheers,
Stan H.