A Canadian zoo started with 16 whooping cranes and planned to hatch 20 chicks a year. A few birds were kept for breeding and the rest released into the wild. At the end of last year, a total of 136 cranes had spent some time in the zoo. If the pattern continues, how many cranes will have spent time in the zoo by the end of this year? by the end of next year?

898

To find out how many cranes will have spent time in the zoo by the end of this year, we need to determine how many cranes are added each year.

In the first year, the zoo had 16 whooping cranes. It also planned to hatch 20 chicks a year. So, the total number of cranes at the end of that year is 16 (original) + 20 (hatched) = 36 cranes.

In the second year, some birds were kept for breeding, which means they were not released into the wild. Let's assume they kept "x" birds for breeding. This means the remaining (36 - x) cranes were released into the wild.

At the end of the second year, the total number of cranes in the zoo is (16 + 20 + x) cranes, and the total number of cranes that spent time in the zoo (including those released into the wild) is (36 - x) cranes.

Given that a total of 136 cranes had spent some time in the zoo by the end of the last year (the end of the second year), we can set up an equation:

(16 + 20 + x) + (36 - x) = 136

By simplifying that equation, we find:

52 + x = 136

Subtracting 52 from both sides of the equation, we get:

x = 84

So, in the second year, the zoo kept 84 birds for breeding.

Now, to find out how many cranes will have spent time in the zoo by the end of this year, we need to add the number of birds hatched this year (20) to the number of birds kept for breeding last year (84), and then add the number of birds released into the wild last year (36 - 84 = -48). Since negative birds don't make sense, we consider this as zero.

Therefore, the total number of cranes in the zoo at the end of this year would be:

(16 + 20 + 84) + 0 = 120

So, by the end of this year, there would be 120 cranes that spent time in the zoo.

To find out how many cranes will have spent time in the zoo by the end of next year, we will follow a similar approach. We add the number of birds hatched next year (20) to the number of birds kept for breeding this year (84) and the number of birds released into the wild this year (36 - 84 = -48, considering as zero):

(16 + 20 + 84) + 0 = 120

So, by the end of next year, there would be 120 cranes that spent time in the zoo.