2. Ten large marbles weigh the same as 14 small marbles. How many large marbles weigh the same as 35 small marbles?

To solve the problem, we start by establishing a relationship between the weights of large marbles and small marbles. Let: - \( L \) be the weight of one large marble. - \( S \) be the weight of one small marble. From the information given, we know that: \[ 10L = 14S \] To find the weight of one large marble in terms of small marbles, we can rearrange this equation: \[ L = \frac{14S}{10} = \frac{7S}{5} \] Now, we want to find out how many large marbles weigh the same as 35 small marbles. The total weight of 35 small marbles is: \[ 35S \] We need to find \( x \), the number of large marbles that weigh the same as 35 small marbles: \[ xL = 35S \] Substituting \( L \) from our earlier equation: \[ x \left(\frac{7S}{5}\right) = 35S \] Now, we can simplify this equation: \[ \frac{7xS}{5} = 35S \] Dividing both sides by \( S \) (assuming \( S \neq 0 \)): \[ \frac{7x}{5} = 35 \] To eliminate the fraction, multiply both sides by 5: \[ 7x = 175 \] Now, divide both sides by 7: \[ x = \frac{175}{7} = 25 \] Thus, the number of large marbles that weigh the same as 35 small marbles is: \[ \boxed{25} \]