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The difference of the digits of a 2-digit number is 1. Five times the sum of the digits plusone is equal to the number. Find the number. |
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Answer» Two digits, a, bthen10a + b = the number:"the difference of digits of two digit number is 1."a - b = 1:"five times the sum of the number plus one is equal to the number."5(a+b) + 1 = 10a + b5a + 5b + 1 = 10a + b5a - 10a + 5b - b = -1-5a + 4b = -1:Use substitution here, multiply the 1st equation by 4, add to the 2nd eq+4a - 4b = 4-5a + 4b = -1 addition eliminates b, find a-a = 3a = -3find b-3 - b = 1-b = 1 + 3-b = 4b = -4:The number-3(10) + (-4) = -34 is the number::Usually not a neg answer in these problems, see if this works in the statement:"five times the sum of the number plus one is equal to the number."5(-3 + (-4)) + 1 = -345(-7) + 1 = -34-35 + 1 = -34; confirms our solution of -34 |
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