In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
4 years
Let the number of daisy plants after x years be represented by 6 + 3x - 2(x-1) = 6 + 3x - 2x + 2 = 4 + x.
Let the number of jasmine plants after x years be 26 - 2x.
We need to solve for x when the number of daisy plants equals the number of jasmine plants:
4 + x = 26 - 2x
3x = 22
x = 4 years.
Thus, the correct answer is option 2: 4 years.
Important Questions from Arithmetic Progression
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
