Answer:
Step-by-step explanation:
x - an integer
then: 2x is an even number and 2x+1 is an odd number
consecutive odd numbers increase by 2 (even numbers too)
so the next odd number (the middle number) is:
2x+1+2 = 2x+3
and the third (the largest) consecutive is:
2x+3+2 = 2x+5
the sum of the smallest and the middle numbers is:
2x + 1 + 2x + 3
3 times the largest number is:
3(2x + 5)
the sum of the smallest number and middle number is 27 less than 3 times the largest number, so:
2x + 1 + 2x + 3 = 3(2x + 5) - 27
4x + 4 = 6x + 15 - 27
-6x -6x
-2x + 4 = -12
-4 -4
-2x = -16
÷(-2) ÷(-2)
x = 8
2x+1 = 2•8+1 = 17
2x+3 = 2•8+3 = 19
2x+5 = 2•8+5 = 21
Check:
2x+1+2x+3 = 16+1+16+3 = 36
36+27 = 63
63:3 = 21 = 2x+5
