I am an array made with 24 tiles.My number of rows is 2 More than the number of tiles in each of my rows. How many rows do I have?
Let's solve this step by step.
Let's assume the number of tiles in each row is x.
According to the given information, the total number of tiles can be calculated as follows:
Total number of tiles = number of rows * number of tiles in each row
So, we have the equation: 24 = (x + 2) * x
Expanding the equation, we get: 24 = x^2 + 2x
To solve this quadratic equation, we can rearrange it to:
x^2 + 2x - 24 = 0
Now, we can factorize or use the quadratic formula to solve for x.
Using the quadratic formula, x can be calculated as:
x = (-2 ± √(2^2 - 4 * 1 * -24)) / (2 * 1)
Simplifying further, we have:
x = (-2 ± √(4 + 96)) / 2
x = (-2 ± √100) / 2
x = (-2 ± 10) / 2
Now, we have two possible solutions for x:
x1 = (-2 + 10) / 2 = 8 / 2 = 4
x2 = (-2 - 10) / 2 = -12 / 2 = -6
Since we're considering the number of tiles in each row, the number cannot be negative. Therefore, we discard the negative value -6.
So, the number of tiles in each row (x) is 4.
To find the number of rows, we add 2 to the number of tiles in each row:
Number of rows = x + 2 = 4 + 2 = 6
Therefore, you have 6 rows.
To determine the number of rows in your array, we need to find a value that satisfies the given conditions. Let's break down the information provided:
- You have an array consisting of 24 tiles.
- The number of rows is 2 more than the number of tiles in each row.
Let's assume the number of tiles in each row is "x."
According to the given information, the number of rows is "x + 2".
To find the value of "x," we can set up an equation based on the total number of tiles:
Total number of tiles = Number of rows * Number of tiles in each row
Expressing this equation with the given information:
24 = (x + 2) * x
Now, we'll solve this equation to find the value of "x" and determine the number of rows.
24 = x^2 + 2x
Rearranging the equation:
x^2 + 2x - 24 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, we can factor it:
(x + 6)(x - 4) = 0
This equation can be satisfied if either (x + 6) = 0 or (x - 4) = 0.
If (x + 6) = 0, then x = -6. However, the number of tiles or rows cannot be negative in this context, so we discard this solution.
If (x - 4) = 0, then x = 4.
Therefore, the number of tiles in each row (x) is 4, and the number of rows is (x + 2) = 6.
So, you have 6 rows in your array.
n(n-2) = 24
n^2 - 2 n - 24 = 0
(n-6)(n+4) = 0
n = 6