Question

Hi solve this please

Answer 1

Answer:

120 days

Step-by-step explanation:

(i)

Given that jenny will use the club every alternate day.

1,3,5,7,9,11,...359.

Let the number of days jenny used the club be 'n'.

a(n) = a + (n - 1) * d

359 = 1 + (n - 1) * 2

359 - 1 = (n - 1) * 2

358 = 2n - 2

360 = 2n

n = 180.

(ii)

Given that Sally will use the club every third day.

1,4,7,10,13..358

Let the number of days sally used the club be 'm'.

a(m) = a + (m - 1) * d

358 = 1 + (m - 1) * 3

358 - 1 = (m - 1) * 3

360 = 3m

m = 120

As u can see, Jenny and Sally use the club together on every 6th day.

Let the numbers used by both be 'p'.

1,7,13, ... 355.

⇒ 355 = 1 + (p - 1) * 6

⇒ 355 - 1 = 6p - 6

⇒ 354 = 6p - 6

⇒ p = 60

Therefore:

Number of days both went to club = 180 + 120 - 60 = 240

Number of days neither went to club = 360 - 240 = 120.

Hope it helps!