One-third the sum of a number N and 5 is 2 more than one-fifth the sum of N and 3.

N= ?

1/3 (N+5)-2=1/5 (N+3)

check that.

Do i mulitply the equation my 5,3?

yes, multipy both sides by 15

To solve this equation, we'll break it down into smaller steps:

Step 1: Translate the given information into an equation:
"One-third the sum of a number N and 5" can be represented as (1/3)(N + 5).
"Is" means equal, so we have:
(1/3)(N + 5) = "2 more than" = (1/5)(N + 3) + 2.

Step 2: Simplify the equation:
To remove the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of 3 and 5, which is 15:
15 * (1/3)(N + 5) = 15 * [(1/5)(N + 3) + 2].

This simplifies to:
5(N + 5) = 3(N + 3) + 30.

Step 3: Solve the equation:
Distribute on both sides:
5N + 25 = 3N + 9 + 30.

Combine like terms:
5N + 25 = 3N + 39.

Subtract 3N from both sides:
5N - 3N + 25 = 3N - 3N + 39.

This simplifies to:
2N + 25 = 39.

Subtract 25 from both sides:
2N + 25 - 25 = 39 - 25.

This simplifies to:
2N = 14.

Finally, divide both sides by 2:
2N/2 = 14/2.

This simplifies to:
N = 7.

So, the value of N is 7.