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 2 of 2: Solve the equation for y. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two places.

Answer 1

If the unknown number is y, then:

18 times y → 18y

18y minus 97 → 18y - 97

9 less than a number → y - 9

So, the given word problem can be written into this equation.

`18y-97=y-9`

To solve for y, here are our steps:

1. Subtract "y" on both sides.

`\begin{gathered} 18y-y-97=y-y-9 \\ 17y-97=-9 \end{gathered}`

2. Add 97 on both sides of the equation.

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

3. Divide both sides of the equation by 17.

`\begin{gathered} (17y)/(17)=(88)/(17) \\ y=(88)/(17)\approx5.18 \end{gathered}`

Hence, the value of y is 88/17 or approximately 5.18.