A pair of consecutive integers has the property that 7 times the smaller is less than 6 times the greater. What Are the greatest such integers?
If you could tell me how u got your answers i would appreciate it as i have a test on it tomorrow and do not understand it.
2006-08-01 09:50:27 · 8 answers · asked by nicluvswings 3 in Science & Mathematics ➔ Mathematics
Ylu have been given the solution, leading to
x < 6
One respondant didn't note that the problem asked for integers (mentioning 5.999...)
Sometimes it is helpful to see the truth
x 7x x+1 6(x+1)
- -- ---- -------
1...7....2......12 (dots used for alignment)
2..14...3......18
3..21...4......24
4..28...5......30
5..35...6......36
6..42...7......42
As soon as we hit 6, the inequality is no longer true.
5 and 6 is the greatest pair
2006-08-01 10:42:43 · answer #1 · answered by Anonymous · 0⤊ 0⤋
When they give you a problem about consecutive numbers, make the first number "x" and the second number "x + 1"
Then go from there:
"7 times the smaller " means
7*x
"6 times the greater" means
6(x + 1)
"7 times the smaller is less than 6 times the greater" means:
7*x < 6(x + 1)
7x < 6x + 6
x < 6
The greatest integer possible, then, for "x" has to be 5, since x is always less than 6.
So,
x = 5
and x + 1 = 6
2006-08-01 18:37:46 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Okay - are you ready? Let's call the 2 numbers x and y. Since we know they are consecutive integers, then it follows that x+1=y (assuming that x is the smaller of the 2). With me so far? Now if you set up the equation:
7x < 6y => 7x < 6(x+1) => 7x < 6x+6 => x < 6.
Therefore, the greatest set of such integers is 5 and 6.
Any other questions - you can email me at minddancer4u@yahoo.com.
2006-08-01 16:58:48 · answer #3 · answered by minddancer4u 1 · 0⤊ 0⤋
The derivation that 7x<6(x+1) giving that x<6 is correct.
Just for fun you can check the answer as follows:
7*5=35 6*6=36 It works
7*6=42 6*7=42 (of course)
7*7=49 6*8=48
2006-08-01 17:38:33 · answer #4 · answered by odu83 7 · 0⤊ 0⤋
i think this is it...
pair of consecutive integers = x (smaller) and x+1 (larger)
7x < 6(x+1)
7x < 6x+6
subtract 6x from both sides
x < 6
so the greatest integers would be just under 6....so 5.999, and the other one would be that plus 1, so 6.999
study hard and good luck!
2006-08-01 16:57:27 · answer #5 · answered by Anonymous · 0⤊ 0⤋
The greater integer is x, the smaller one is x-1.
7(x-1) < 6x
7x - 7 < 6x
x - 7 < 0
x < 7
The greater integer is 6; the smaller one is 5.
Th
2006-08-01 17:31:38 · answer #6 · answered by Thermo 6 · 0⤊ 0⤋
7x<6(x+1)
7x<6x+6
x<6
There you go. (By the way, x is the smaller number)
2006-08-01 17:07:55 · answer #7 · answered by RandomNormality 3 · 0⤊ 0⤋
I like pogo.
2006-08-01 16:53:35 · answer #8 · answered by cool 1 · 0⤊ 0⤋