Question

a farmer grew a giant pumpkin for the county fair. she chose a plant with a healthy pumpkin and watered it carefully. the pumpkin gained the same amount of weight each week. three weeks later, the pumpkin weighed 141 pounds. after seven more weeks, the pumpkin weighed 372 pounds. how much weight did the pumpkin gain per week?

pounds per week
complete the equation that describes the relationship between the pumpkins weight, w, and the elapsed time in weeks, t.
write your answer using whole numbers or decimals rounded to the nearest tenth.
w = t +

Explanation:

Step1: Find weight gain per week

Let \( r \) be the weekly weight gain. In 7 weeks, the weight gain is \( 7r \). The initial weight (at \( t = 3 \) weeks) is 141 pounds, and at \( t = 3 + 7 = 10 \) weeks, it's 372 pounds. So, \( 372 - 141 = 7r \). Calculate \( 372 - 141 = 231 \), then \( r=\frac{231}{7}=33 \) pounds per week.

Step2: Find the initial weight (at \( t = 0 \))

At \( t = 3 \), \( W = 141 \). Using \( W = rt + b \) (where \( b \) is initial weight), \( 141 = 33\times3 + b \). Calculate \( 33\times3 = 99 \), so \( b = 141 - 99 = 42 \).

Step3: Form the equation

The equation is \( W = 33t + 42 \).

Answer:

33 (for weight gain per week)
\( W = 33t + 42 \) (for the equation, with the first box being 33 and the second box being 42)