Question

at a pumpkin patch, if armando guesses the weight of his pumpkin within 0.3 pounds, he gets to take the pumpkin home for free. if his pumpkin weighs 4.9 pounds, which two equations can be used to find the minimum and maximum weights he can guess in order to get his pumpkin for free?
$x + 4.9 = 0.3$ and $x + 4.9 = -0.3$
$x - 4.9 = 0.3$ and $x - 4.9 = -0.3$
$x - 0.3 = 4.9$ and $x - 0.3 = -4.9$
$x + 0.3 = 4.9$ and $x + 0.3 = -4.9$

Explanation:

Step1: Understand the problem

We need to find the minimum and maximum guess weights \( x \) such that the difference between \( x \) and the actual weight \( 4.9 \) is at most \( 0.3 \). Mathematically, this means \( |x - 4.9|=0.3 \).

Step2: Solve the absolute - value equation

The absolute - value equation \( |x - 4.9| = 0.3 \) can be split into two cases:

• Case 1: \( x-4.9 = 0.3 \) (when \( x-4.9\geq0 \))
• Case 2: \( x - 4.9=- 0.3 \) (when \( x - 4.9<0 \))

So the two equations that can be used to find the minimum and maximum weights are \( x - 4.9 = 0.3 \) and \( x - 4.9=-0.3 \)

Answer:

\( x - 4.9 = 0.3 \) and \( x - 4.9=-0.3 \) (the second option in the given set of options)