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The ratio of two numbers is $2:3$. when 6 is subtracted from the smaller of the two numbers and 7 is added to the larger of the two, the new ratio is $2:7$. what was the smaller of the two numbers before 6 was subtracted from it

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sqdancefan

Answer:

  14

Step-by-step explanation:

Let the smaller and larger numbers be represented by S and L, respectively.

  S/L = 2/3 . . . . the original ratio of the numbers

  3S = 2L . . . . . multiply by 3L

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  (S-6)/(L+7) = 2/7 . . . . the new ratio of the numbers

  7(S-6) = 2(L+7) . . . . . multiply by 7(L+7)

  7S -42 = 2L +14

Using the expression for 2L from the first ratio, we can substitute to get ...

  7S -42 = 3S +14 . . . . substitute 3S for 2L

  4S = 56 . . . . . . . . . . .add 42-3S

  S = 14 . . . . . . . . . . . . . divide by 4

The original smaller number was 14.

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