A worker produces 1092 units in 3 days. If the production is expected to increase by 20% each day, compute the total number of units produced on first day and last day.
Let's find the number of units produced on the first day.
The production increases by 20% each day, so on the second day, the worker would produce 1092 + 1092 * 20/100 = 1092 + 218.4 = 1310.4 units.
On the third day, the worker would produce 1310.4 + 1310.4 * 20/100 = 1310.4 + 262.08 = 1572.48 units.
Therefore, on the first day, the worker would produce 1092 - 218.4 - 262.08 = 611.52 units.
The total number of units produced on the first day and last day is 611.52 + 1572.48 = <<611.52+1572.48=2184>>2184 units. Answer: \boxed{2184}.
To compute the total number of units produced on the first day, we need to find the value before the first day's increase of 20%.
Let's assume the number of units produced on the first day is x. Then, on the second day, there is an increase of 20%, resulting in 1.2x units produced. Similarly, on the third day, there is another increase of 20%, resulting in (1.2)*(1.2)x = 1.44x units produced.
Given that the worker produces 1092 units over the three days, we can set up the equation:
x + 1.2x + 1.44x = 1092
Combining like terms, we have:
3.64x = 1092
Dividing both sides of the equation by 3.64, we find:
x = 300
Therefore, the worker produced 300 units on the first day (without any increase).
To compute the total number of units produced on the last day, we need to find the value after the third day's increase of 20%.
We know that on the third day, the worker produced 1.44x units. To find the units produced on the last day, we need to multiply 1.44x by another 20% increase:
(1.44x)*(1.2) = 1.728x
Therefore, the worker produced 1.728 times the units produced on the first day on the last day. Substituting x = 300 into the equation, we find:
1.728 * 300 = 518.4
Hence, the total number of units produced on the last day is 518.4.
To find the total number of units produced on the first day, we need to back calculate from the given information.
Let's assume the number of units produced on the first day is x.
On the second day, the production is expected to increase by 20%. So, the number of units produced would be 1.2 * x.
On the third day, the production is expected to increase by 20% again. So, the number of units produced would be 1.2 * (1.2 * x) = 1.44 * x.
Given that the worker produces 1092 units in total over the three days, we can write an equation to solve for x:
x + 1.2x + 1.44x = 1092
Combining like terms, we get:
3.64x = 1092
Dividing both sides by 3.64, we can solve for x:
x = 1092 / 3.64
x ≈ 300
So, the worker produced approximately 300 units on the first day.
To find the total number of units produced on the last day, we can use the same logic:
On the third day, the worker produced 1.44 * x units, where x is the number of units produced on the first day.
Substituting the value of x we found earlier:
1.44 * 300 ≈ 432
Therefore, the worker produced approximately 432 units on the last day.