Question
When the digits are swapped, the new two-digit number
equals 44 less than 120% of the original. The sum of the digits is 13. Determine the original number.Solution
Let tens = x, units = y. Original = 10x + y; swapped = 10y + x. 10y + x = 1.2(10x + y) − 44 1.2 = 6/5 ⇒ multiply by 5: 50y + 5x = 60x + 6y − 220 ⇒ 55x − 44y = 220 … (I) x + y = 13 … (II) Multiply (II) by 44 and add to (I): (55x − 44y) + (44x + 44y) = 220 + 572 ⇒ 99x = 792 ⇒ x = 8 y = 13 − 8 = 5 Original number = 10×8 + 5 = 85
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