Find 4 consecutive even integers such that twice the least increased by the greatest is 96........I got 10,12,14and 16 but not sure...please help!
let the 4 consecutive even integers be
x, x+2, x+4, and x+6
so 2x + x+6 = 96
3x = 90
x = 30
So the 4 integers are 30,32,34, and 36
check : is twice the smallest plus the largest equal to 98
2(30) + 36 = 96
YeS!
You could have known your numbers are not correct by testing them.
If I understand the question, 10, 12, 14 and 16 is not right.
Is 2 * 10 + 16 = 96?
Call the numbers a, b, c, d. We're really only interested in a and d.
How much bigger is d than a?
d = a + ?
Call the unknown x. d = a + x
Now, we know that 2a + d = 96
but we also know that d = a + x
So 2a + a + x = 96
3a = 96 - x
To find four consecutive even integers, let's assume the first integer as "x". Since the integers are consecutive, the second integer would be (x + 2), the third would be (x + 4), and the fourth would be (x + 6).
According to the problem, twice the least (2x) increased by the greatest (x + 6) equals 96. We can set up an equation to solve for x.
2x + (x + 6) = 96
Combining like terms:
3x + 6 = 96
Subtracting 6 from both sides:
3x = 90
Dividing both sides by 3:
x = 30
Therefore, the first even integer is 30. The consecutive even integers would be 30, 32, 34, and 36.
To find four consecutive even integers, we can let the first even integer be represented by "x." Since the problem states that we need four even consecutive integers, we can also represent the next three even integers as "x + 2," "x + 4," and "x + 6."
According to the problem, twice the least (2x) increased by the greatest (x + 6) is equal to 96. This can be written as the equation:
2x + (x + 6) = 96
Now we can solve for x.
Combining like terms:
3x + 6 = 96
Subtracting 6 from both sides:
3x = 90
Dividing both sides by 3:
x = 30
Now, to find the four consecutive even integers, we substitute the value of x back into the representation we established earlier:
x = 30
x + 2 = 30 + 2 = 32
x + 4 = 30 + 4 = 34
x + 6 = 30 + 6 = 36
Therefore, the four consecutive even integers that satisfy the given condition are 30, 32, 34, and 36.