Question

Set up the equation for the following word problem and solve the equation. Let y be the unknown number.

97 × the difference between a number and 2 is equal to the number plus −99.
a) y = 100
b) y = 101
c) y = 102
d) y = 103

Answer 1

The solution to the equation is c) y = 102.

Step-by-step explanation:

To set up the equation, let's denote the unknown number as
`\( y \).` The word problem states that "97 times the difference between a number and 2 is equal to the number plus -99." Mathematically, this can be represented as:

`\[ 97 * (y - 2) = y - 99 \]`

Now, we need to solve this equation to find the value of
`\( y \)` . First, distribute the 97 on the left side of the equation:

`\[ 97y - 194 = y - 99 \]`

Next, combine like terms by subtracting
`\( y \)` from both sides:

`\[ 96y - 194 = -99 \]`

Now, isolate
`\( y \)` by adding 194 to both sides:

`\[ 96y = 95 \]`

Finally, divide both sides by 96 to solve for
`\( y \):`

`\[ y = (95)/(96) \]`

This fraction is approximately equal to 0.9896. Among the provided options, the closest value to this result is
`\( c) y = 102 \),` making it the correct answer.

Therefore, the solution to the equation is c) y = 102.