Question

Find two consecutive odd numbers such that the sum of the larger number and twice the smaller number is 27 less then foir times the smaller number

Answer 1

29 and 31

Explanation:

x - some integer

2x+1 - an odd integer (the smaller one)

2x+1+2=2x+3 - the next odd integer consecutive to 2x+1 (the larger)

2×(2x+1) - twice the smaller number

2x+3+2•(2x+1) -the sum of the larger number and twice the smaller number

4•(2x+1) - four times the smaller number

4•(2x+1)-27 - 27 less then four times the smaller number

2x + 3 + 2•(2x + 1) = 4•(2x + 1) - 27

2x + 3 + 4x + 2 = 8x + 4 - 27

6x + 5 = 8x - 23

-5 -5

6x = 8x - 28

-8x -8x

-2x = - 28

÷(-2) ÷(-2)

x = 14

2x+1 = 2•14 + 1 = 29

2x+3 = 2•14 + 3 = 31

Check: 31+2•29=31+58=89; 4•29-27=116-27=89