+0  
 
0
53
3
avatar

Anton has two species of ants, Species A and Species B, in his ant farm. The two species are identical in appearance, but Anton knows that every day, there are twice as many ants of Species A than before, while there are three times as many ants of Species B. On Day 0, Anton counts that there are 30 ants in his ant farm. On Day 5, Anton counts that there are 3281 ants in his ant farm. How many of these are of Species A?

Guest Sep 28, 2017

Best Answer 

 #1
avatar+4694 
+2

Let  a  be the number of species A ants he had to begin with.

Let  b  be the number of species B ants he had to begin with.

 

On day 0 there are  a + b ants.

On day 1 there are  2a + 3b  ants.

On day 2 there are  2 * 2a + 3 * 3b  ants.

On day 3 there are  2 * 2 * 2 * a + 3 * 3 * 3 * b  ants.

On day 4 there are  24 * a + 34 * b  ants.

On day n there are  2n * a + 3n * b

So...

On day 5 there are 25 * a + 35 * b

 

a + b  =  30     →     b = 30 - a

 

25 * a  + 35 * b  =  3281

 

25 * a + 35 * (30 - a)  =  3281

 

25a + 35 * 30 - 35a  =  3281

 

25a - 35a  =  3281 - 35 * 30

 

a(25 - 35)  =  3281 - 35 * 30

 

a  =  (3281 - 35 * 30) / (25 - 35)

 

a  =  19

 

So...he started with  19  ants of species A.

After  5 days, he will have  2* 19  =  608 ants of species A.

hectictar  Sep 28, 2017
edited by hectictar  Sep 29, 2017
Sort: 

3+0 Answers

 #1
avatar+4694 
+2
Best Answer

Let  a  be the number of species A ants he had to begin with.

Let  b  be the number of species B ants he had to begin with.

 

On day 0 there are  a + b ants.

On day 1 there are  2a + 3b  ants.

On day 2 there are  2 * 2a + 3 * 3b  ants.

On day 3 there are  2 * 2 * 2 * a + 3 * 3 * 3 * b  ants.

On day 4 there are  24 * a + 34 * b  ants.

On day n there are  2n * a + 3n * b

So...

On day 5 there are 25 * a + 35 * b

 

a + b  =  30     →     b = 30 - a

 

25 * a  + 35 * b  =  3281

 

25 * a + 35 * (30 - a)  =  3281

 

25a + 35 * 30 - 35a  =  3281

 

25a - 35a  =  3281 - 35 * 30

 

a(25 - 35)  =  3281 - 35 * 30

 

a  =  (3281 - 35 * 30) / (25 - 35)

 

a  =  19

 

So...he started with  19  ants of species A.

After  5 days, he will have  2* 19  =  608 ants of species A.

hectictar  Sep 28, 2017
edited by hectictar  Sep 29, 2017
 #2
avatar+76821 
+1

Very nice, hectictar.....!!!!!

 

 

 

cool cool cool

CPhill  Sep 28, 2017
 #3
avatar+4694 
+1

Yeaa!! I got it right!!!!!!!!!!! laughlaughlaughlaugh

hectictar  Sep 28, 2017

7 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details