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 – 0.3 = 4.9 and x – 0.3 = –4.9
x + 0.3 = 4.9 and x + 0.3 = –4.9
x + 4.9 = 0.3 and x + 4.9 = –0.3
x – 4.9 = 0.3 and x – 4.9 = –0.3

Please answer correctly

Answer 1

To find the minimum and maximum weights that Armando can guess to still win the pumpkin, we start with the actual weight of the pumpkin, which is 4.9 pounds. He can guess within 0.3 pounds of this weight.

This means his guess \( x \) must satisfy the following inequalities:

\[
4.9 - 0.3 < x < 4.9 + 0.3
\]

This simplifies to:

\[
4.6 < x < 5.2
\]

To determine the equations corresponding to these inequalities, we can formulate two equations:

1. For the lower limit:
\[
x - 0.3 = 4.9 \quad \text{(for the lower bound)}
\]

2. For the upper limit:
\[
x + 0.3 = 4.9 \quad \text{(for the upper bound)}
\]

Therefore, the correct equations to represent the minimum and maximum weights he can guess to get the pumpkin for free are:

\[
x - 0.3 = 4.9 \quad \text{and} \quad x + 0.3 = 4.9
\]

These equations correspond to the first option you provided. Thus, the answer is:

**x – 0.3 = 4.9 and x + 0.3 = 4.9**.