I don't think I am understanding this question.
Question:
A zoo started with 16 cranes and panned to hatch 20 chicks. A few birds were kept for breeding and the rest realeased 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 there be by the end of this year? the next year?
My thinking:
I don't know how many cranes they kept so I called that 'x'
I know they hatch 20 cranes a year so the number of years it took to get to 136 cranes would be 136/20 = 6.8 years
So by the end of the year would be 7 years so 20 x 7 = 140 cranes
So by the end of next year would be 140 + 20 = 160
planned to hatch 20 chicks a year* CORRECTION
The equation would actually be 16+(n-1)(20) because they initially started off with 16 cranes so 16=a and they increase every year by 20 cranes so d=20 so plug the values into a+(n-1)d. There would be 156 cranes at the end of this year and 176 by the next year.
Your thinking is definitely on the right track! Let me explain the steps you took in finding the solution to the problem.
First, you correctly observed that you need to determine how many cranes were kept for breeding. Let's call this number "x".
Next, you noted that the zoo started with 16 cranes and hatched 20 chicks each year. So the total number of cranes in a given year would be the sum of the cranes from the previous year and the 20 new chicks hatched in that year, minus any birds that were kept for breeding. This can be represented as: Previous year's cranes + 20 - x.
Since you are given that at the end of the last year, there were a total of 136 cranes in the zoo, you can set up an equation based on this information: 16 + 20(6.8) - x = 136.
Solving for x, you'll find that x ≈ 159.2. But since you can't have a fraction of a bird, you would assume that the number of cranes kept for breeding was approximately 159.
To find the number of cranes by the end of this year, as you correctly mentioned, it would be 20 multiplied by the number of years (7 years) plus the initial 16 cranes: 20 * 7 + 16 = 156 cranes.
Finally, to find the number of cranes by the end of next year, you add 20 (the number of chicks hatched each year) to the number of cranes by the end of this year: 156 + 20 = 176 cranes.
So, by the end of this year, there will be approximately 156 cranes, and by the end of next year, there will be approximately 176 cranes.