The second of two number is 5 times first. their sum is 42 . find both numbers

Hey there!

To start, first let the variable, x, represent your first unknown number. Now, because the second number is 5 times the first, this will be represented as 5x (you simply multiply 5 to your variable of the first number, x). 

Now, since the sum of the two numbers are 42, you can represent this by setting up this equation:
5x+x=42

Combine your like terms (terms of the same variable and are raised to the same power):
5x+x=42
6x=42

Divide both sides by 6 to solve for x:
6x/6=42/6
x=7

Because x represents the first number, your first number would be 7. 

Now, since the second number is 5 times the first, you can find the second number by multiplying x by 5:
x=7
7*5=35

Your second number is 35.

To check if both numbers are correct, you can add your first number, 7 to your second number, 35, to see if you get 42 since you know their sum must be 42:
7+35=42

Therefore, your final answer would be that the first number is 7, and the second number is 35.

Hope this helps, and have a marvelous day! :)

Hello there!

We need to give these unknown numbers a name. We can call the first number x and the second number y.

y = 5x
x+y = 42

In order to solve this thing, we just need to substitute y in 5x in the second equation.

x + y = 42

x + 5x = 42

6x = 42

x= 42/6

x = 7

Now we found the first number, we gonna use it to help us find the second number.

y = 5x

y = (5)(7)

y = 35

The numbers are x = 7 and y = 35

I hope this helps!

Let me know if you have questions about the answer :)