Four times the larger of two consecutive even integers is ten less than the smaller
What is the larger of these two numbers
let the first even integer be x
then the next even integer is x+2
4(x+2) < x by 10
4x + 8 + 10 = x
3x = -18
x = -6
so the smaller is -6 and the larger is -4
check:
4 times the larger = -16
the smaller is -6
is -16 less than -6 by 10? YES
Let's call the larger of the two consecutive even integers "x".
The smaller of the two consecutive even integers can be represented as x - 2.
According to the given information,
4 times the larger, which is 4x, is ten less than the smaller, which is (x - 2).
So, we can set up the equation:
4x = (x - 2) - 10
Now, let's solve for x:
4x = x - 12
Subtracting x from both sides, we get:
3x = -12
Dividing both sides by 3, we find:
x = -4
Therefore, the larger of the two consecutive even integers is -4.
To solve this problem, let's first translate what the statement is saying into equations:
Let's assume that the larger even integer is represented by x, and the smaller even integer is represented by x+2 (since they are consecutive even integers).
According to the statement, "Four times the larger of two consecutive even integers is ten less than the smaller," we can write the equation:
4x = (x+2) - 10
Now, let's solve the equation to find the value of x, which represents the larger even integer:
4x = x - 8
Subtracting x from both sides of the equation:
3x = -8
Dividing both sides by 3:
x = -8/3
Now we have found the value of x, which is approximately -2.67. However, the problem asks for the larger even integer. Since x represents the larger even integer, we can conclude that the larger even integer is -2.67.
However, it's important to note that even integers are only whole numbers, so in this case, there is no valid solution for this problem.