The difference between two numbers is 6, and 5 times the smaller number is 3 times the larger number. Find the smaller number.

9514 1404 393

  9

Step-by-step explanation:

Let x and y represent the two numbers, with y being the smaller.

  x - y = 6 . . . . . . difference is 6

  3x = 5y . . . . . . . 3 times the larger is 5 times the smaller

Use the first equation to write an expression to substitute for x:

  x = y + 6

  3(y +6) = 5y

  18 = 2y . . . . . . .subtract 3y and collect terms

  9 = y

The smaller number is 9.

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