In an HDB kitchen tile pattern, the ratio of the number of cream tiles to the number of grey tiles is $A : B = 2 : 3$. The ratio of grey tiles to teal tiles is $B : C = 4 : 5$. Find the ratio $A : B : C$ in its SIMPLEST FORM.
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Worked Solution
Step 1: Identify the bridge term. $B$ appears in both ratios but with different values: $B = 3$ in the first, $B = 4$ in the second. We must scale to make them equal.\n
Step 2: Find LCM$(3, 4) = 12$. This is our target value of $B$.\n
Step 3: Scale the first ratio. $A : B = 2 : 3$, multiply by $4$ to get $A : B = 8 : 12$.\n
Step 4: Scale the second ratio. $B : C = 4 : 5$, multiply by $3$ to get $B : C = 12 : 15$.\n
Step 5: Combine. $A : B : C = 8 : 12 : 15$.\n
Step 6: Check simplest form. $\\gcd(8, 12, 15) = 1$, so $8 : 12 : 15$ is already simplest.\nVerify: $A : B = 8 : 12 = 2 : 3$ ✓ and $B : C = 12 : 15 = 4 : 5$ ✓.
Answer: 8 : 12 : 15
Correct answer: 8 : 12 : 15
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