Question

Write the statement for the problem in mathematical language. Use x for the tens digit and y for the unit digits in the two digit numbers. Find the two-digit number which is 2 times the sum of its digits

Answer 1

Answer:

  18

Step-by-step explanation:

A two-digit number (xy) will have the value 10x+y. The sum of its digits is x+y.

You want ...

  10x +y = 2(x +y)

  1 ≤ x ≤ 9

  0 ≤ y ≤ 9

The equation can be simplified to ...

  8x = y

The only single-digit values for x and y that satisfy the requirements are ...

  x = 1, y = 8

The two-digit number of interest is 18.

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Check

Its sum of digits is 1+8 = 9. 2×9 = 18.

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Comment on the relationship in the problem

Many of us learned our multiplication tables for 9s by remembering that the sum of digits of 9n was 9, and that the leading digit of the product was n-1.