The sum of two numbers is 32. one of the numbers is 4 less than 5 times the other. what are the numbers?

Let the first number be = x

Then other number according to question is

4 less than 5 times the number i.e. 5x-4

Also ,sum of numbers is 32

x+5x-4=32

6x-4=32

Add 4 to both sides

6x-4+4=32+4

6x=36

Divide both sides by 6

x=36/6

x=6

First number =x =6

Other number =5(6)-4 = 30-4 =26

26 and 6

Step-by-step explanation: Let's use two variables to represent our two numbers in this problem. Since a variable is a letter that represents any number, we can pick any letters we want to but I will use with x and y.

So if the sum of two numbers is 32, that means x + y = 32.

To solve for two separate variables, we will need two separate equations. So for the second equation, let's read through the second sentence in the problem.

"One of the numbers" that's x, "is" means equals, "4 less than 5 times the other" is not 4 - 3y, it means 5y - 4. The word "less than" switches the order around. So we now have x = 5y - 4.

So to solve this system of equations, let's use substitution. Since x = 5y - 4, we can substitute a 5y - 4 in for x in the first equation to get (5y - 4) + y = 32. Solving from here we get 6y - 4 = 32 by combining like terms. Now we can get rid of that -4 by adding 4 to both sides of the equation to get 6y = 36. Now, we will divide both sides of the equation by 6 in order to isolate y and we end up with y = 6.

To find x, plug 6 back in for y in the second equation to get x = 5 (6) -4 which we can simplify to x = 30 - 4 which simplifies to x = 26.

Therefore, our two numbers in this problem are 26 and 6.

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