mary an jim have tickets to a concert. mary`s ticket number is one less than jim`s ticket number. the product of their numbers is 812. what are the two numbers?
(x)(x-1) = 812
This is impossable, as an odd number added to an even number always yeilds an odd. the numbers would need to have 1/2 in them, tickets don't have those.
That said, you can devide 812 by 2, subtract 1/2 or .5 from one ticket number and add it to the other.
lela collected postcards
28,29
To solve this problem, let's take the following steps:
1. Set up the equation: Tickets with numbers x and (x-1) have a product of 812. So, the equation is x*(x-1) = 812.
2. Simplify the equation: Multiply x with x-1 on the left side of the equation, giving us x^2 - x = 812.
3. Rearrange the equation: Bring all terms to one side, x^2 - x - 812 = 0.
4. Factorize the quadratic equation: To find the two numbers, we need to factorize the quadratic equation. We can do this by either completing the square or using the quadratic formula. Let's use the quadratic formula.
The quadratic formula is given as: x = (-b ± sqrt(b^2 - 4ac)) / 2a.
For our equation x^2 - x - 812 = 0, we have a = 1, b = -1, and c = -812.
Plugging these values into the quadratic formula, we get:
x = (1 ± sqrt((-1)^2 - 4*1*(-812))) / 2*1.
Simplifying further, we have:
x = (1 ± sqrt(1 + 3248)) / 2.
x = (1 ± sqrt(3249)) / 2.
5. Calculate the two possible values of x: Taking the positive square root (given that ticket numbers cannot be negative), we have:
x = (1 + sqrt(3249)) / 2.
Evaluating this expression further, we find:
x ≈ 28.247.
As we mentioned earlier, tickets don't have decimal numbers, so we need to round this number down to the nearest whole number.
The possible value for x is 28.
6. Calculate the other ticket number: To find Mary's ticket number (x-1), we subtract 1 from x.
Mary's ticket number ≈ 28 - 1 = 27.
So, the two possible ticket numbers are 28 and 27. However, as mentioned earlier, these are not realistic ticket numbers since they have decimal parts. Tickets typically have only whole numbers. Therefore, in this case, it seems that there is no valid solution.