the sum of 3 less than 5 times a number and the number increased by 9 is 24. what is the number?

Answer 1

Hi Marilynn! First let's write "3 less than 5 times a number" as an expression, then we'll write "the number increased by 9" as an expression, and add these up so they equal 24.

When you see the word "a number," you can think of this as a variable; we'll use n

The first part of the equation is 3 less than 5 times n. 5 times n can be written as 5n. 3 less than 5n is 5n-3.

The second part of the equation is n increased by 9, which is n+9.

We sum them up to get (5n-3)+(n+9). This is equal to 24, so we write (5n-3)+(n+9)=24.

Now we're going to use algebra to simplify and solve this. We want to add up like terms, so we'll add the n terms together. 5n+n=6n. Then we can add the numbers together: -3+9=6. Putting this together, you get:

6n+6=24

To get n by itself, we'll first subtract 6 from both sides:

6n=18

Last step here, we'll divide by 6 on both sides to get:

n=3