a, b, c, d and e are distinct integers such that (5−a)(5−b)(5−c)(5−d)(5−e)=28. What is the value of a+b+c+d+e?

well, since the only factors of 28 are ±1,±2,±4,±7 I'd have to go with

(2)(-2)(1)(-1)(7)
(5-3)(5-7)(5-4)(5-6)(5-(-2)) = 28
3+7+4+6-2 = 18

thanks...

To find the value of a + b + c + d + e, we need to determine the values of a, b, c, d, and e first.

The given equation is (5 − a)(5 − b)(5 − c)(5 − d)(5 − e) = 28.

Since 28 is a small number, we can try out different combinations of distinct integers (a, b, c, d, e) such that their product equals 28.

Let's start by considering the factors of 28: 1, 2, 4, 7, 14, and 28.

We can assign a value to one of the variables, say a.
If we set a = 1, then the equation becomes (5 − 1)(5 − b)(5 − c)(5 − d)(5 − e) = 28.

Now, let's check if any combination of (b, c, d, e) can satisfy this equation.
When a = 1, the equation becomes (4)(5 − b)(5 − c)(5 − d)(5 − e) = 28.

By trying out different values for b, c, d, and e, we can find out if any combination satisfies the equation. For example:

If we set b = 2, then the equation becomes (4)(3)(5 − c)(5 − d)(5 − e) = 28.

If we set c = 4, then the equation becomes (4)(3)(1)(5 − d)(5 − e) = 28.

If we set d = 7, then the equation becomes (4)(3)(1)(−2)(5 − e) = 28.

If we set e = 14, then the equation becomes (4)(3)(1)(−2)(−9) = 28, which is true.

Therefore, we have found a combination that satisfies the equation when a = 1, b = 2, c = 4, d = 7, and e = 14.

Now, we can find the value of a + b + c + d + e:
1 + 2 + 4 + 7 + 14 = 28.

So, the value of a + b + c + d + e is 28.