Question

Set up the equation for the following word problem and solve the equation. Let y be the unknown number.18 times a number minus 97 is equal to 9 less than the number.Step 1 of 2: Write out the equation.

Answer 1

Hello there. To solve this question, we'll have to remember some properties about set up an equation and solving them.

"Let y be an unknown number. 18 times a number minus 97 is equal to 9 less than the number."

We need to find this number.

Starting with the equation:

`18y-97=y-9`

On the left hand side, we have 18y as 18 times the number, then subtracted 97 for the minus 97 part. On the right hand side, 9 less than the number is represented as the number minus 9.

So, subtract y - 97 on both sides of the equation

`\begin{gathered} 18y-97-(y-97)=y-9-(y-97) \\ 18y-97-y+97=y-9-y+97 \\ 17y=88 \end{gathered}`

Divide both sides of the equation by a factor of 17

`\begin{gathered} (17y)/(17)=(88)/(17) \\ \\ y=(88)/(17) \end{gathered}`

This is the number we've been looking for.