3.66
The problem 3.66 asks:
"На складе 18,5 т веревочного троса в бухтах. Сколько таких бухт было на складе, если после покупки 12 таких бухт осталась 12,85 т?"
This translates to:
"The warehouse has 18.5 tons of rope in coils. How many such coils were in the warehouse if, after buying 12 such coils, 12.85 tons remain?"
Let's solve it step by step.
Let \( x \) be the number of original coils.
The weight of each coil is given by the total weight divided by the number of coils: \( \frac{18.5}{x} \).
When 12 coils are bought, 12.85 tons remain, so:
\[ 18.5 - 12 \left(\frac{18.5}{x}\right) = 12.85 \]
Solving for \( x \):
\[ 18.5 - \frac{222}{x} = 12.85 \]
\[ \frac{222}{x} = 18.5 - 12.85 \]
\[ \frac{222}{x} = 5.65 \]
\[ x = \frac{222}{5.65} \]
Calculate \( x \):
\[ x \approx 39.29 \]
Since the number of coils must be a whole number, we round 39.29 to the nearest whole number, which is 39.
Thus, there were approximately 39 coils on the warehouse initially.
