Question

If $a:b = 1:3$ and $b$ is a positive, one-digit integer, what is the greatest possible value of $a$?

Answer 1

Answer is 3

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Work Shown:

a:b = 1:3

a/b = 1/3

a*3 = b*1 ... cross multiply

3a = b

b = 3a

Since b is a one digit number, this means that the largest it can get is 9

`b \le 9\\\\3a \le 9\\\\a \le (9)/(3)\\\\a \le 3`

The largest possible value of 'a' is 3