Question

Given that a:b = 3:7 and a:c = 4:3 Find the ratio a:b:c

Answer 1

The combined ratio a:b:c, given a:b = 3:7 and a:c = 4:3, is found by equalizing the 'a' across both ratios to form a new combined ratio of 12:28:9, which simplifies to 4:7:3.

Step-by-step explanation:

The student has given two separate ratios, a:b = 3:7 and a:c = 4:3, and needs to find the combined ratio a:b:c. To solve this, we need to make sure each variable is represented by the same units across the ratios.

Step-by-step solution:

1. Equalize the a-term in both ratios. This can be achieved by finding a common multiple of the first terms of the given ratios (3 of a:b and 4 of a:c). The least common multiple of 3 and 4 is 12.
2. Multiply both parts of the first ratio a:b by 4 to get 12:28.
3. Multiply both parts of the second ratio a:c by 3 to get 12:9.
4. Now that the a-term is consistent, you can easily combine them to form the compound ratio a:b:c = 12:28:9.

Therefore, the combined ratio of a:b:c is 12:28:9, which simplifies to 4:7:3 when all terms are divided by their greatest common divisor, in this case, 3.

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