What are the numbers?

When two numbers are added together the result is 45. Twice the greater number is six more than five times the lesser number. What are the numbers?

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x = lesser number
45 - x = greater number   {the sum of the two numbers is 45}

2(45 - x) = 5x + 6  {twice the greater is six more than five times the lesser}
90 - 2x = 5x + 6   {used distributive property}
7x = 84   {added 2x and subtracted 6 from each side}
x = 12   {divided each side by 7}
45 - x = 33   {substituted 12, in for x, into 45 - x}

12 and 33 are the two numbers

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