(7/30+1/2+4/15):(49/50-14/25-2/5)=

To solve the expression \((7/30 + 1/2 + 4/15) : (49/50 - 14/25 - 2/5)\), we can start by simplifying both the numerator and the denominator separately.

Step 1: Simplifying the Numerator

The numerator is \(7/30 + 1/2 + 4/15\).

1. Find a common denominator. The least common multiple (LCM) of \(30\), \(2\), and \(15\) is \(30\).

2. Rewrite each fraction with the common denominator:

   • \(1/2 = 15/30\)
   • \(4/15 = 8/30\)

3. Add the fractions:

\[ 7/30 + 15/30 + 8/30 = (7 + 15 + 8)/30 = 30/30 = 1 \]

So, the numerator simplifies to \(1\).

Step 2: Simplifying the Denominator

The denominator is \(49/50 - 14/25 - 2/5\).

1. Find a common denominator. The LCM of \(50\), \(25\), and \(5\) is \(50\).

2. Rewrite each fraction with the common denominator:

   • \(14/25 = 28/50\)
   • \(2/5 = 20/50\)

3. Subtract the fractions:

\[ 49/50 - 28/50 - 20/50 = (49 - 28 - 20)/50 = 1/50 \]

So, the denominator simplifies to \(1/50\).

Step 3: Final Calculation

Now we can evaluate the expression:

\[ 1 : (1/50) = 1 \times (50/1) = 50 \]

Thus, the final result is:

\[ \boxed{50} \]