Question

The top 50 poultry farmers in town put together all the eggs they could produce in one day to donate to families in need. Each farmer produced the same number of eggs more than the farmer below them in rank. If Marivic is on top with 5 900 eggs and Rico is on 50th with 1 000 eggs, how many eggs did all 50 farmers put together for donation?

6. Which formula will help you get the answer the fastest?




7. How many eggs did all 50 farmers put together for donation?

A. 120 050 eggs

C. 169 050 eggs

B. 147 500 eggs

D. 172 500 eggs
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Answer 1

Answer:

D) 172 500 eggs

Step-by-step explanation:

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Answer 2

Given: The top 50 poultry farmers in town put together all the eggs they could produce in one day to donate to families in need. Each farmer produced the same number of eggs more than the farmer below them in rank. Marivic is on top with 5900 eggs and Rico is on 50th with 1 000 eggs.

To find: 1- Formula to get the answer

2- Total eggs put together by the farmers

Solution: Here, the first one donates 5900 eggs and the last one donates 1000 eggs. Since each farmer produced the same number of eggs more than the farmer below them in rank, it forms an arithmetic progression (A.P.).

Let the first term be a1, the last term be an and total number of farmers be n.

Since there are 50 farmers, n= 50

First farmer donates 5900 eggs, a1 = 5900

Last farmer donates 1000 eggs, an = 1000

The formula for calculating the sum of terms when first and last terms are given is:

$\frac{n}{2} (a1 + an)$

Using values:

$= \frac{50}{2} (5900 + 1000)$

$= 25 \times 6900$

= 172500 eggs

Therefore, the formula to get the answer is option (c) $\frac{n}{2} (a1 + an)$ and total number of eggs donated is option (d) 172500 eggs.