I cashed a check
By mistake the cashier gave me cents instead of dollars and dollars instead of cents. I spent five cents on the way home, and then discovered that i possessed exactly twice the amount of the check. What was the exact amount on the check ?
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though he received y dollars and x cents
after spending 5 cents, his money is twice the amount on the check, i.e. 100y+x -5 = 2(100x + y)
98y = 199x + 5
we need to find two numbers in the exact multiple series of 98 and 199 which differs by 5.
98’s multiple series: 98,196,294,392,490,588,686,784,882,980,1078,1176,1274,1372,1470,1568,1666,1764,1862,1960,2058,2156,2254,2352,2450,2548,2646,2744,2842,2940,3038,3136,3234,3332,3430,3528,3626,3724,3822,3920,4018,4116,4214,4312,4410,4508,4606,4704,4802,4900,4998,5096,5194,5292,5390,5488,5586,5684,5782,5880,5978,6076,6174
199’s multiple series: 199,398,597,796,995,1194,1393,1592,1791,1990,2189,2388,2587,2786,2985,3184,3383,3582,3781,3980,4179,4378,4577,47764975,5174,5373,5572,5771,5970,6169,6368,6567,6766,6965,7164,7363,7562,7761,7960,8159,8358,8557,8756,8955,9154,9353,9552,9751,9950
98*63 = 199*31 +5
thus the amount on the check was 31 dollar and 63 cents.