If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is?

Question

If one-half of one integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the 2 integers?

Answer 1

Let's say that your integer is "n." The next consecutive integer is n+1.

"Three-fifths of the next consecutive integer" is (n+1)*3/5. "One-half of [the] integer" is n/2.

If the difference is three, it means that:

((n+1)*3/5) - (n / 2) = 3
6(n+1) - 5n = 30 (multiply by 10 to remove fractions)
6n+6 - 5n = 30
n = 24

Now, let's check that result:

If "one integer" is 24, and "the next consecutive integer" is 25...

(3/5 of 25) - (1/2 of 24) = 3 ?
15 - 12 = 3

It works out, so the answer is correct.

Answer 2

1/2 of X is subtracted from the 3/5 of (X + 1), the difference is 3. (3/5) * (X+!) - (1/2) * X = 3 (3X / 5) + (3 / 5) - X / 2 = 3 3X / 5 - X / 2 = 3 - (3 / 5) (6X - 5X) /10 = (15 - 3) / 5 X / 10 = 12 / 5 X = (10 * 12) /5 X = 120 / 5 = 24 ============= Hence, 24 and 25 are the required consecutive numbers. Verification ; (3/5)*25 - 24/2 15 - 12 = 3 =============

Answer 3

Let integers be x and x + 1
(3/5).(x + 1) - (1/2).x = 3
6x + 6 - 5x = 30 (upon X by 10)
x = 24
Integers are 24 and 25

Answer 4

We want 3/5*(x+1) - ½(x). But
3/5 -1/2 = 1/10,
so the diffrence is 1/10 * x + 3/5 = (x+6)/10.
So your problem says
(x+6)/ 10 = 3
x+6 = 30
x = 24
x+1 = 25.
Let's check: ½ * 24 = 12
3/5 * 25 = 15
15 -12 = 3. Done!