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Linear Equations in One Variable

SAT Math· difficulty 5/5

A two-digit number's digits sum to 9. Reversing them gives a number 27 less. What is the original number?

  • A

    36

  • B

    63

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  • C

    45

  • D

    54

Explanation

Let tens =a= a, ones =b= b. a+b=9a + b = 9. Original =10a+b= 10a + b, reversed =10b+a= 10b + a. (10a+b)−(10b+a)=27(10a + b) - (10b + a) = 27 → 9a−9b=279a - 9b = 27 → a−b=3a - b = 3. With a+b=9a + b = 9: a=6a = 6, b=3b = 3. Number = 63.

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