I have been working on this forever and I am not sure how to do this:) Find two consecutive intergers such that the sum of 8 times the first interger and 7 times second interger is 127.
Thank you very much in advance, also if you would not mind explaining the steps so I will understan what is going on.
2006-11-25 15:14:18 · 10 answers · asked by Jeff D 1 in Science & Mathematics ➔ Mathematics
Let the first integer be x.
The next consecutive integer is x+1.
Now setup the equation.
8(x) + 7(x+1) = 127.
8x + 7x + 7 = 127.
15x + 7 = 127.
15x = 120
x = 8.
This means that the integers are 8 and 9.
To check, 8 times 8 is 64. 7 times 9 is 63. 64 + 63 = 127.
It checks out!
2006-11-25 15:17:55 · answer #1 · answered by hokiejthweatt 3 · 0⤊ 0⤋
Let x and y be the integers. Then
8x+7y = 127.
I shall write down the equation for consecutivity. Then when I get the solution, I will see if the answers x and y are integers.
If y succeeds x, then x+1 = y. Two equations in two unknowns:
8x+7y = 127
-x + y = 1
(the last equation is obtained by subtracting x from both sides of y = x+1)
Multiply the second equation by 8:
8x+7y = 127
-8x+8y = 8
Add these:
0x + 15y = 135
15y = 135
Divide both sides by 15:
y = 9
y = x+1, or 9 = x+1, or 9 - 1 =x, so x = 8
Are 8 and 9 integers? They are. So they constitute a solution. Check to see if these work in the original equations - they do.
So there's the answer: 8 and 9.
2006-11-25 23:29:27 · answer #2 · answered by alnitaka 4 · 0⤊ 0⤋
First number = x
Second number = x + 1
8 times x ( for the first number)
7 times (x + 1) (for the second number)
first + second = answer
Know let's solve
8x + 7(x+1) = 127
8x + 7x + 7 = 127 --7(x+1) = 7x + 7
15x + 7 = 127 -- 8x+7x = 15x
15x + 7 -7 = 127-7 --subtract 7 on both sides
15x = 120 -- 127-7 = 120
15x/15 = 120/15 --divide 15 on both sides
x = 8 -- 120/15 = 8
first consecutive number: x = 8
second consecutive number: x+1=9
2006-11-25 23:25:16 · answer #3 · answered by goobersandpopcorn 2 · 0⤊ 0⤋
Call the integers x and x+1 (since they are consecutive). Then from the problem we have that
8x + 7(x+1) = 127 Now multiply
8x + 7x + 7 = 127 Combine terms
15x + 7 = 127 Subtract 7 from both sides
15x = 120 Divide both sides by 15
x = 8
So the integers are 8 and 9.
Hope that helps.
Doug
2006-11-25 23:31:40 · answer #4 · answered by doug_donaghue 7 · 0⤊ 0⤋
The numbers are 8 and 9. Solve the equations below
x + 1 = y
8 + 1 = y
9 = y
8x + 7y = 127
8x + 7(x+1) = 127
8x + 7x + 7 = 127
15x + 7 = 127
15x = 120
x = 8
2006-11-25 23:20:44 · answer #5 · answered by Redcarn 5 · 0⤊ 0⤋
Let X = the first integer
Then X+1 is the other integer
8X + 7*(X+1) = 127
8X + 7X + 7 = 127
15X + 7 = 127
15X = 120
X = 8
The two integers are 8 and 9
2006-11-25 23:23:44 · answer #6 · answered by z_o_r_r_o 6 · 0⤊ 0⤋
Let x = the smaller integer
Your two consecutive numbers would be x and (x+1)
From the problem:
8x + 7(x+1) = 127
Distribute and solve for x.
8x + 7x + 7 = 127
15x = 120
x = 8
Your two numbers are 8 and 9.
Hope that helped.
2006-11-25 23:20:58 · answer #7 · answered by Anonymous · 0⤊ 0⤋
The answer is 8 and 9:
8 x 8 = 64
9 x7 = 63
63+64 = 127
(I just kept filling in the numbers until it worked - sorry!)
2006-11-25 23:17:55 · answer #8 · answered by Anne 4 · 0⤊ 0⤋
1. 8a + 7b = 127
2. a+7=b substitute this in the equation for b
3. 8a + 7a+7=127
4. Subtract 7 from both sides
5. 15a=120
6. Divide both sides by 15
7. a=8
8. b=8+1
9. b=9
2006-11-25 23:21:39 · answer #9 · answered by Anonymous · 0⤊ 1⤋
You are given that 8*x + 7*(x+1) = 127
So, expanding, 15*x +7 = 127
Thus 15*x = 120
and then x = 24
2006-11-25 23:25:34 · answer #10 · answered by geek31459 2 · 0⤊ 0⤋