Answer :
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.
[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.