Find the ratio a: b, if 2a−b/6 = b/3

a:b = 2

Step-by-step explanation:

Here we need to operate with terms in order to arrive to a ratio a:b (or a/b).

We have:

2a−b/6 = b/3

Lets sum b/6 in both sides:

2a−b/6 + b/6 = b/3 + b/6

2a = b/3 + b/6

Now, we can multiply and divide b/3 by 2 to make a 6 appear on the denominator and sum it with b/6, this is, use common denominator:

2a = b/3*(2/2) + b/6

2a = 2b/6 + b/6

2a = 3b/6

2a = b/2, as 3/6 = 1/2

Now lets divide both sides by b to make an a/b appear:

2a/b = (b/2)/b

2a/b = 1/2

Finally, multiply both sides by (1/2) or divide by 2:

(2a/b)/2 = 2

a/b = 2

This is, a is twice as b. If b is 1 so a is 2; if b is 45 so a is 90, and so on.

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