The smallest of three consecutive integers is added to twice the largest, the result so obtained is fifteen less than four times the middle integer. Find the integer s.
let the 3 numbers be x, x+1, and x+2
2(x+2) + x = 4(x+1) - 15
solve for x, then sub into my definitions
Let's solve this problem step by step.
Let's assume the smallest integer is x.
According to the problem, the three consecutive integers will be x, x + 1, and x + 2.
Now let's translate the given information into an equation.
"The smallest of three consecutive integers is added to twice the largest."
This can be represented as x + 2(x + 2).
"The result so obtained is fifteen less than four times the middle integer."
This can be represented as 4(x + 1) - 15.
Now we can set up the equation:
x + 2(x + 2) = 4(x + 1) - 15.
Simplifying the equation:
x + 2x + 4 = 4x + 4 - 15.
Combine like terms:
3x + 4 = 4x - 11.
Rearranging the variables:
3x - 4x = -11 - 4.
Simplifying:
-x = -15.
Multiply both sides by -1 to isolate x:
x = 15.
Therefore, the smallest integer, x, is 15.
Please let me know if I can help you with anything else.
To solve this problem, let's first assign variables to the three consecutive integers.
Let's call the smallest integer "x". So the other two consecutive integers will be "x + 1" and "x + 2".
According to the problem, the smallest integer is added to twice the largest integer:
x + 2(x + 2)
The result obtained is fifteen less than four times the middle integer:
= 4(x + 1) - 15
Now we can set up the equation:
x + 2(x + 2) = 4(x + 1) - 15
Simplifying the equation step by step:
x + 2x + 4 = 4x + 4 - 15
3x + 4 = 4x - 11
Moving all terms involving "x" to one side and the constants to the other side:
4 + 11 = 4x - 3x
15 = x
Therefore, the smallest integer (x) is 15.