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?

**x = lesser number**

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

45 - x = greater number

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**

**Ask the House**