The sum of two numbers is 28. The larger is two less than two times the smaller. Find the two numbers.?

Question

Help. :(

Answer 1

18+10=28

The correct answer is 18 and 10.

Answer 2

Lets make the larger number x and the smaller number y. We can form algebraic equations taking the problem one sentence at a time. Then we can solve the problem using those equations.

The first sentence tells us that x + y = 28. Lets call this equation 1.

If we take x as being the larger number then the second sentence tells us that if we increase y(the smaller number) to twice its size, then subtract two, we will get the larger number x. In terms of the variables we are using:

(larger number) x = 2y - 2
Lets call this equation 2

We can then substitute for x in our equation 1 to resolve the problem as follows:

x + y = 28
(but x = 2y - 2, so rewriting the equation gives us the next line)
(2y - 2) + y = 28
2y - 2 + y = 28
grouping like terms
2y + y = 28 +2 (2 changes sign when it crosses the = sign)
3y = 30
y = 30/3
y = 10

Now that we have an answer for our smallest number 'y' we can substitute that value in our equation 2 (or 1) to arrive at an answer for our lager value.

x = 2y -2
but y = 10
therefore
x = (2x10) - 2
x = 20 -2
x = 18

The two numbers are 10 and 18

Answer 3

First, you need to know algebraic terminology. It says the sum of two numbers is 28, so ( n ) + ( n )=28. Those spaces are for any extra info. Next, it says that the larger one (since we read left to right, I suggest that you use the first one) is equal to two less (subtract 2) and two times (multiply by 2) the smaller (keep n for the second). Lastly, set it to equal to 28. Altogether:
1) ( n ) + ( n )=28
2) (2n ) + ( n )= 28
3) (2n-2)+ ( n )=28
4) (2n-2)+(n)=28
5) 3n-2=28
6) 3n-2(+2)=28(+2)
7) 3n=30
8) 3n/3=30/3
9) n=10
10) [2(10)-2] + 10=28
11) [20-2]+10=28
12) 18+10=28
13) The larger number is 18, while the smaller number is 10.

Answer 4

the first person is right.. if you want to see the work.. see below.

#1.........28= x+y (<---- sum of two numbers is 28)
#2..........x= 2y - 2 (<----- the LARGER is two less than two times the smaller)

...so plug it in.. the equation #2, into equation #1.

..28= 2y - 2 + y..

28= 3y - 2 ..then add two to both sides..
+2 +2

30= 3y
y= 10
............
go back to equation #1 .. and plug "y=10" into the problem; and then solve.
28= x + 10
-10 -10

18 = x

..therefore x= 18 , and y= 10..

Answer 5

let x and y be the numbers.
x+y=28 -- (1)
x=2y-2 (if x is the larger)
(1) becomes 2y-2+y=28
3y-2=28
3y=30
y=10
x=18 (is the larger 2 less than 2 times the smaller?)

Answer 6

x + y = 28
x = 2y - 2
2y - 2 + y = 28
3y = 30
y = 10
x = 18
Numbers are 18 and 10

Answer 7

x + 2x - 2 = 28
3x - 2 = 28
3x = 30
x = 10
28 - 10 = 18
The two numbers are 10 and 18.