Question

A veterinarian is changing the diets of two animals simba and cuddles.simba currently consumes 1200 calories per day. that number will increase 100 calories each day.cuddles currently consumes 3230 calories a day. that number will be decreased by 190 calories each day.the pattern will continue until both animals are consuming the same number of calories each dayin how many days will that be?how many calories will each animal be consuming each day then?

Answer 1

1200 + 100d = 3230 - 190d
100d + 190d = 3230 - 1200
290d = 2030
d = 2030/290
d = 7

1200 + 100(7) = 1200 + 700 = 1900
3230 - 190(7) = 3230 - 1330 = 1900

They will be consuming the same amount on day 7.....they will both consume 1900 calories

Answer 2

On the eighth day of diet both animals will be having same calories.

1900 calories each animal will be consuming each day.

Explanation:

1) Diet sequence of Simba :

1200, 1300, 1400......

a = 1200, d = 100

The nth term in Arithmetic sequence is given as:

`a+(n-1)d=a_n`

`1200+(n-1)100=a_n`...(1)

2) Diet sequence of Simba :

3230,3040,2850......

a' = 3230, d' = 190

`a'-(n'-1)d'=a_n'`

`3230-(n'-1)190=a_n'`...(2)

The pattern will continue until both animals are consuming the same number of calories . So,
`a_n =a_n'`

(1) = (2)

`1200+(n-1)100=3230-(n'-1)190`

n = 8

On the eighth day of diet both animals will be having same calories.

Calorie consumed on eighth day:

`1200+(8-1)100=a_n=1900`

`3230-(8-1)190=a_n'=1900`

1900 calories each animal will be consuming each day.