Question

Connie collected 50 seashells during her 5 day vacation. Each day she collected 3 more than the previous day. How many seashells did she find each day?

Answer 1

Answer:

First day, N(1) = 4

Second day, N(2) = 4 + 3 = 7

Third day, N(3) = 4 + 6 = 10

Fourth day, N(4) = 4 + 9 = 13

Fifth day, N(5) = 4 + 12 = 16

Step-by-step explanation:

She spent 5 days on her vacation.

She collected 50 seashells in those days. Each day she collected 3 more than the previous day.

We can represent this with an arithmetic progression:

N(n) = x + 3(n - 1)

Where x is the amount of sea shells collected on the first day.

n = the particular day

So, for the five days day:

N(1) = x + 3(1 - 1) = x + 3(0) = x

N(2) = x + 3(2 - 1) = x + 3(1) = x + 3

N(3) = x + 3(3 - 1) = x + 3(2) = x + 6

N(4) = x + 3(4 - 1) = x + 3(3) = x + 9

N(5) = x + 3(5 - 1) = x + 3(4) = x + 12

The sum of all the sea shells is 50:

N(1) + N(2) + N(3) + N(4) + N(5) = 50

=> x + x + 3 + x + 6 + x + 9 + x + 12 = 50

5x + 30 = 50

5x = 50 - 30 = 20

x = 20 / 5

x = 4

Therefore:

First day, N(1) = 4

Second day, N(2) = 4 + 3 = 7

Third day, N(3) = 4 + 6 = 10

Fourth day, N(4) = 4 + 9 = 13

Fifth day, N(5) = 4 + 12 = 16