Question

The sum of two numbers is 120÷5. The 1st number is 3 times that of the 2nd number. Find the two numbers. Write an equation to show your work. Does anyone know how to do this question?

Answer 1

`18` and `6`

Explanation:

Let’s use two variables to represent the numbers in this problem. I’ll use `x` and `y`.

So the sum of the two numbers `=`

`120/5=24`

So this means that

`x+y=24`

To solve for two variables, we need two separate equations. The second sentence in the problem says the first number is `3` times the second number. I’ll say variable `x` is the first number and `y` is the second number.

`x=3y`

So now we have a system of equations. We can either use elimination or substitution. Substitution seems like the most efficient way to solve this so I’ll go with that.

Because we already have `x=3y`, let’s make

`x=24-y` ←from the first equation

So now `x` equals two things. That means those two things `=` each other. Let’s set up an equation that represents that:

`3y=24-y`

Now we need to isolate the consonant and the variable on different sides. Add `y` to both sides:

`3y+y=24`

`4y=24`

Now let’s solve for `y`. Divide both sides by `4`

`y=6`

And now we have the second number (or first number, it really does not matter).

Now we can substitute `6` for `y` in `x=3y`

`x=3(6)`

`x=18`

Now we have both numbers! Let’s double-check to see if we’re right by adding them together:

`18+6=24`

And it looks like we got the answers! Hope this helped!