Read the following text and answer the following questions on the bas...
Let the workers are x, Number of boxes prepared by the workers
= 2 + 3x
According to the question,
x(2 + 3x) = 85
⇒ 3x2 + 2x – 85 = 0
⇒ 3x2 + 17x – 15x – 85 = 0
⇒ x(3x + 17) – 5(3x + 17) = 0 ⇒
⇒ (3x + 17)(x – 5) = 0
⇒ x = 5
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Read the following text and answer the following questions on the bas...
Given:
- A small scale industry produces a certain number of boxes of candles in a day.
- The number of boxes prepared by each worker on a particular day was 2 more than thrice the number of workers.
- The total number of boxes produced in a particular day was 85.
To Find:
The number of workers working in the industry.
Solution:
Let's assume the number of workers in the industry as 'x'.
Number of boxes prepared by each worker:
According to the given information, the number of boxes prepared by each worker on a particular day was 2 more than thrice the number of workers. Mathematically, we can represent it as:
Number of boxes prepared by each worker = 3x + 2
Total number of boxes produced:
The total number of boxes produced in a particular day was given as 85.
So, we can set up the following equation:
Total number of boxes = Number of workers * Number of boxes prepared by each worker
85 = x * (3x + 2)
Solving the equation:
We need to solve the quadratic equation to find the value of 'x'.
85 = x * (3x + 2)
85 = 3x^2 + 2x
3x^2 + 2x - 85 = 0
To solve this quadratic equation, we can either factorize it or use the quadratic formula. Let's use the quadratic formula:
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Here, a = 3, b = 2, and c = -85.
Substituting the values in the quadratic formula, we have:
x = (-2 ± sqrt(2^2 - 4(3)(-85))) / (2 * 3)
x = (-2 ± sqrt(4 + 1020)) / 6
x = (-2 ± sqrt(1024)) / 6
x = (-2 ± 32) / 6
Simplifying further, we have:
x = (30/6) or (-34/6)
x = 5 or -17/3
Since the number of workers cannot be negative or in fractions, we can conclude that the number of workers working in the industry is 5 (option A).
Therefore, the correct answer is option A.
Read the following text and answer the following questions on the bas...
How many
boxes will be prepared when the number of workers are increased by 2
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