4200:72:24:100•5+1700-900:400

To simplify the expression \(4200:72:24:100\cdot 5 + 1700 - 900:400\), we will break it down step by step.

1. Interpret the colons and operations: The colons (:) in your expression can be treated as division. Thus, we rewrite the expression:

   \[ \frac{4200}{72} \cdot \frac{24}{100} \cdot 5 + 1700 - \frac{900}{400} \]

2. Simplify \( \frac{900}{400} \): \[ \frac{900}{400} = \frac{9}{4} = 2.25 \]

3. Calculate \( \frac{4200}{72} \): \[ \frac{4200}{72} = 58.33 \quad (\text{approximately}) \]

4. Calculate \( \frac{24}{100} \): \[ \frac{24}{100} = 0.24 \]

5. Combine the results: Now we multiply: \[ 58.33 \cdot 0.24 \cdot 5 \]

   First, \( 58.33 \cdot 0.24 \): \[ 58.33 \cdot 0.24 \approx 14 \]

   Now multiply by 5: \[ 14 \cdot 5 = 70 \]

6. Now add \( 1700 \): \[ 70 + 1700 = 1770 \]

7. Finally, subtract \( 2.25 \): \[ 1770 - 2.25 = 1767.75 \]

Thus, the final result of the expression \(4200:72:24:100\cdot 5 + 1700 - 900:400\) is approximately \( 1767.75 \).