Algebra three more than a number is 21. find the number. five times the sum of smaller number and the larger number is 21. what are the numbers? the sum of three numbers is 41. the 2nd number is twice the 1st number increased by three and the third number is 9 less than 5 times the first. what are the numbers?

The two numbers are 11 and 28.

If this is homework, be sure to show your work.

Let x be the smallest number.
Let x + 2 be the other number (consecutive even integer)

Now to translate the rest;)
three times the smaller 3(x)
19 more -19
sum of the two integers - (x) +( x+2)

Pulling it together,
3x -19 = x + x +2
collect like terms
3x - 19 = 2x + 2
Put all the constants on one side by adding 19 to both sides.
3x - 19 +19= 2x + 2 + 19
3x = 2x +21
Subtract 2x from both sides to have all the x's on one side.
3x - 2x = 2x +21 - 2x
x = 21
The other number is 21 + 2, or 23
Check:three times the smaller = 3 x 21 = 63
sum of the two integers = 21 + 23 or 44
is 63 at least 19 more than 44

Given the incomplete statement of the problem, any two different numbers will work.

Given any two different numbers, the larger number is more than the smaller one and their sum is ___.

Let x be the number
You have 5x=x-3
4x=-3 and x=-3/4
Check
5*(-3/4)=? -3/4 -3=-(3+12)/4=-15/4
It checks.

24 and 25

8 and 12

The two numbers are 9 and 27.

Solution:
Suppose the two numbers are x and y, then,

x + y = 36 ---------1
and
x = 3y -------------2

Solving equation 1 and 2...

3y+y=36 => 4y=36 => y = 9
x + 9 = 36 => x = 27

Please rate and comment if my answer is right.

The first is 11, the second is 16 and the third is 48, as far as I know.