Sandi weighs 145 lb and has started a new diet plan that promises a loss of 2 lb per month until reaching a goal weight.

1. Write a linear equation that describes how much Sandi weighs each month.
2. Use your equation to find out how many months it will take Sandi to reach 115 lb.

Use [tex]x[/tex] as the number of months since Sandi started her new diet.

Part 1 of 2

The linear equation that describes how much Sandi weighs each month is [tex]y = 145 - 2x[/tex].

Part 2 of 2

According to the equation, it will take Sandi [tex]\square[/tex] months to reach 115 lb.

We are given that Sandi's weight decreases by 2 lb each month. Her weight after [tex]$ x $[/tex] months is modeled by the equation

[tex]$$
y = 145 - 2x,
$$[/tex]

where [tex]$ y $[/tex] is her weight in pounds after [tex]$ x $[/tex] months.

To find the number of months needed for Sandi to reach 115 lb, we set [tex]$ y = 115 $[/tex] in the equation:

[tex]$$
145 - 2x = 115.
$$[/tex]

Next, subtract 145 from both sides:

[tex]$$
-2x = 115 - 145,
$$[/tex]

which simplifies to

[tex]$$
-2x = -30.
$$[/tex]

Now, divide both sides by [tex]$-2$[/tex]:

[tex]$$
x = \frac{-30}{-2} = 15.
$$[/tex]

Thus, it will take Sandi 15 months to reach 115 lb.