Question

Weighing Pumpkins

Every year at Half Moon Bay, there is a pumpkin contest to see who has grown the largest pumpkin for that year. Last year, one pumpkin grower (who was also a mathematician) brought 5 pumpkins to the contest. Instead of weighing them one at a time, he informed the judges, "When I weighed them two at a time, I got the following weights: 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 pounds." Your task is to find how much each pumpkin weighed.

Answer 1

To find the weight of each pumpkin, we can solve a system of equations using the given weights obtained from weighing the pumpkins two at a time.

Step-by-step explanation:

To find the weight of each pumpkin, we can solve a system of equations using the given weights obtained from weighing the pumpkins two at a time. Let's assign variables to the weights of the pumpkins: let's call the weights x, y, z, w, and v, respectively. We have the following information:

1. x + y = 110
2. x + z = 112
3. x + w = 113
4. x + v = 114
5. y + z = 115
6. y + w = 116
7. y + v = 117
8. z + w = 118
9. z + v = 120
10. w + v = 121

We can solve this system of equations using substitution or elimination method. By solving the system, we find that x = 54, y = 56, z = 58, w = 59, and v = 62. Therefore, the weights of the pumpkins are 54 pounds, 56 pounds, 58 pounds, 59 pounds, and 62 pounds, respectively.