in a sport meet,one sportsman told another :"there are nine fewer of us here than twice the product of our total number ?" how many sportsman were there at the meet?
Let's solve the problem step-by-step:
Let's assume the total number of sportsmen at the meet is "x".
According to the statement, "there are nine fewer of us here than twice the product of our total number," we can represent this as an equation:
x - 9 = 2(x * x)
Simplifying the equation:
x - 9 = 2x^2
Rearranging the equation:
2x^2 - x - 9 = 0
To solve this quadratic equation, we can factor it:
(2x + 3)(x - 3) = 0
Setting each factor equal to zero and solving for x:
2x + 3 = 0, or x - 3 = 0
If 2x + 3 = 0, then:
2x = -3
x = -3/2
Since the number of sportsmen cannot be negative, we disregard this solution.
If x - 3 = 0, then:
x = 3
Therefore, there were 3 sportsmen at the meet.
To solve this problem, we need to translate the given information into algebraic equations and then solve them.
Let's assume the total number of sportsmen at the meet is 'x'. According to the given statement, "there are nine fewer of us here than twice the product of our total number," we can write the equation as:
x = 2 * x * (x - 9)
Now, let's solve this equation step by step:
1. Distribute the 2 to the terms inside the parentheses:
x = 2x^2 - 18x
2. Rearrange the equation, bringing all terms to one side:
2x^2 - 19x = 0
3. Factor out an 'x' from the equation:
x(2x - 19) = 0
Using the zero product property, we have two possible solutions for x:
Solution 1: x = 0
Solution 2: 2x - 19 = 0
Since the number of sportsmen can't be zero (x = 0), we discard that solution.
To find the total number of sportsmen, we need to solve the second equation:
2x - 19 = 0
Adding 19 to both sides:
2x = 19
Dividing both sides by 2:
x = 19 / 2
Therefore, the total number of sportsmen at the meet is 19/2 = 9.5.
However, since it doesn't make sense to have a fraction of a person, we can conclude that there was a mathematical error or an incomplete statement given in the problem.
2N - 9 = N
Solve for N.