Let's solve this step by step.

Problem Breakdown:

• Julia has $\frac{2}{5}$ of the sweets.
• Kayleigh and Lara share the remaining sweets in the ratio $3:4$.

Step 1: Calculate the fraction of sweets left for Kayleigh and Lara

Since Julia has $\frac{2}{5}$ of the sweets, the fraction of sweets left for Kayleigh and Lara is: $1 - \frac{2}{5} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5}$

Step 2: Distribute the remaining sweets between Kayleigh and Lara

Kayleigh and Lara share $\frac{3}{5}$ of the sweets in the ratio $3:4$. To find the individual fractions, we need to divide $\frac{3}{5}$ according to this ratio.

• Total parts in the ratio $3 + 4 = 7$.
• Kayleigh's share is $\frac{3}{7}$ of $\frac{3}{5}$.

Step 3: Calculate Kayleigh’s fraction

Now, multiply the fraction of sweets left with Kayleigh's part of the ratio: $\text{Kayleigh's share} = \frac{3}{7} \times \frac{3}{5} = \frac{9}{35}$

Conclusion:

Kayleigh has $\frac{9}{35}$ of the total sweets.

Would you like any further clarification or details?

Related Questions:

1. How many sweets would Kayleigh have if there were 140 sweets in total?
2. What fraction of the sweets does Lara have?
3. If Julia gives $\frac{1}{5}$ of her sweets to Kayleigh, what fraction of the sweets does Kayleigh have now?
4. What is the total fraction of sweets that Lara and Kayleigh have together?
5. If the sweets were divided among four people instead of three, how would that change the distribution?

Tip:

When working with ratios and fractions, always simplify each step as much as possible before proceeding to the next calculation.