Question

Find four consecutive odd integers such that five times the sum of the first and third integers exceeds four times the sum of the second and last integers by 14.

Answer 1

The answer is not -5, -3, or -1. The answer is 13, 15, 17, 19.

Answer 2

I updated the question!!!!

Answer 3

2x+1 = 1st odd integer
2x+3 = 2nd
2x+5 =3rd
2x+7 = 4th
5(2x+1+2x+5)= 20x+30) is the sum of the 1st & 3rd times 5
4(2x+3+2x+7) =16x+40) is the sum of 2nd & last times 4
20x+30 = 16x + 40 +14
4x = 24
x=6
1st integer is 13
2nd is 15
3rd us 17
4th is 19

Check out: 5 (13 +17) = 4(15+19)+14
150 =150

Answer 4

You knew the answer, did you follow the procedure for solution with understanding?

Answer 5

Why'd you do
2x+1 = 1st odd integer
2x+3 = 2nd
2x+5 =3rd
2x+7 = 4th

Why not just do: x, x + 3, x + 5, x +7

Answer 6

I wanted to insure my results were odd, in case there were even digits that would result in sums differing by 14.

Answer 7

So you could you still do x, x + 2, and so on, or no?

Answer 8

Have you tried it using x, and x+2, etc. It may work just as well.

Answer 9

I can try if you haven't.

Answer 10

It comes to the same thing. But may you please explain to me why the term "exceeds four times... by 14." I thought this meant to add 14 to 10x + 20, but it means to add 14 to 8x + 46.

Answer 11

x = 1st digit
x+2 =2nd
x+4 =3rd
x+6 = 4th
5(x+x+4)=4(x+2+x+6)+14
10x+20=8x+32+14
2x=26
x=13 Yes it works so there are apparently only those numbers that will work, it is easier to do it that way, but I always make sure I have a odd result when looking for odd. lol.

Answer 12

It means that the first sum is larger by 14 than the second sum. So to make them equal you add 14 to the second sum.

Answer 13

Oh, I see now. Thank you for your help! xD

Answer 14

You know when they are asking about even numbers I use 2x to be sure I get even numberts, I guess I am sort of paranoid about numbers.

Answer 15

Good luck with these.

Answer 16

You are most welcome.