One number is two less than a second number. Twice the second number is 8 less than 3 times the first. Find th

Question

One number is two less than a second number. Twice the second number is 8 less than 3 times the first. Find the two numbers.
Pre-algebra - by Mary Lee Vivian, Margaret Thomas - 128 pages
Algebra - by Mary Lee Vivian, Margaret Thomas - 128 pages
The popular educator - by Popular educator

One number is two less than a second number. Twice the second number is 8 less than 3 times the first. Find the two numbers.

Answer 1

Using our information, we need to come up with some equations. So:

1) One number is two less than a second number. If we call the first number x and the second number y, we have;

x = y - 2

2) Twice the second number is 8 less than 3 times the first.

3x - 8 = 2y

Now we have 2 equations:

x = y - 2
3x - 8 = 2y,

and we can plug our new value of x (y - 2) in for the x in our second equation. That gives us:

3x - 8 = 2y
3(y - 2) - 8 = 2y
3y - 6 - 8 = 2y
3y -14 = 2y
-14 = -y
y = 14

Since y = 14, we can plug in to solve for x:

x = y - 2
x = (14) - 2
x = 12.

If we plug in and check it, they should work out.

Does that help?

Answer 2

Let x = first number
y = second number

Set up your equations:

First number is two less than second number:
x = y - 2

Twice the second number is eight less than the three times the first:
2y = 3x - 8

Now you have the following two equations:
x = y - 2
2y = 3x - 8

Since the first equation puts x in terms of y, you can substitute that for x into the second equation:

2y = 3(y - 2) - 8
2y = 3y - 6 - 8
2y = 3y - 14

Subtract 3y from both sides:
2y - 3y = 3y - 14 - 3y
-y = -14

Multiply both sides by -1:
y = 14

Now that you have y, you can find x:

x = y - 2
x = 14 - 2
x = 12

So the first number is 12, and the second number is 14.

You can check this as well: 12 is 2 less than 14, so that works. Also, twice 14 is 28. 8 less than 3 times 12 is 8 less than 36, which is 28. So this works as well.

Answer 3

the numbers are 12 and 14

Answer 4

12 and 14. I ain't gonna go into all the confusing bull about x=y-2. Because 14 is 12 plus 2. 14 times 2 is 28. 28 add 8 is 36. 36 is also what you get when you times 12 by 3. It's in-genius isn't it!

Answer 5

OK

x = y -2 ; 2y=3x-8 - so let's make them consistent

x -y = -2
-3x +2y = -8; multiply top equation by 2

2x - 2y = -4
-3x +2y = -8; now add the two equation (note, y's go away)

-x = -12;
x = 12

Substitute
x -y = -2
12-y = -2
-y = -14
y =14

Check
x (12) is 2 less than y (14) YES and

2(14) is 28 and is 8 less than 3 (12) 36 -- YES!!

Hope that helps.

Answer 6

the first number is x , the second is x+2

2*(x+2) = 8-3x
2x+4 =8-3x
5x = 4
x=4/5

proof first number 4/5 second number14/5

2*14/5=28/5 = 8-12/5 = 40/5-12/5=28/5

Answer 7

let first number be x, second be y

x = y-2

2y = 3x - 8
x = (2y+8)/3


y-2 = (2y+8)/3 (both are values of x)
3y-6 = 2y + 8
y = 14

putting the y = 14 in equation 1
x = y-2
x = 14 -2
x = 12

the numbers are 12 and 14

Answer 8

Let x and y be the numbers
x =y-2 -- (1)
2y=3x-8 -- (2)
from (1) , y=x+2
(2) becomes 2(x+2)=3x-8
2x+4=3x-8
-x=-12
x=12
y=14
12, 14 are the numbers

Answer 9

x=y-2
3x=2y+8



so 3(y-2)=2y+8

y=14
x=12