A bag of marbles at the school CCA stall contains red, blue and green marbles. The ratio of red to blue marbles is $3 : 5$, and the ratio of blue to green marbles is $5 : 7$. What fraction of all the marbles are GREEN?
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Worked Solution
Step 1: Identify the bridge term. Blue appears in BOTH ratios as $5$, so the two ratios are already aligned. No scaling is needed.\n
Step 2: Combine into a single three-quantity ratio. red : blue : green = $3 : 5 : 7$.\n
Step 3: Total parts = $3 + 5 + 7 = 15$.\n
Step 4: Green has $7$ parts out of $15$, so the green fraction = $\\dfrac{7}{15}$.\nCheck: $\\dfrac{3}{15} + \\dfrac{5}{15} + \\dfrac{7}{15} = \\dfrac{15}{15} = 1$, accounting for all marbles. ✓
Answer: 7/15
Correct answer: 7/15
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