If `b ne 0 and (3a +b)/(b ) =(11)/(2),` which of the following could be the value of `a/b` ?

Options

A. `3/2`
B. `7/2`
C. `9/2`
D. It is not possible to determine a value of `a/b.`

Answer

A

Explanation

Rearranging the terms of the equation such that `a/b` is on one side and the constants are all on the other will work for this problem. First, cross-multiply to get rid of the fractions. Then, use inverse operations to isolate `a/b:`
`(3a+b)/(b)=(11)/(2)`
`2 (3a+b) =11b`
`6a+2b=11b`
`6a=9b`
`a = 9/6b`
`a/b=3/2`
The answer is (A).
There is a faster approach. Notice that 2 shows up in the denominator in most of the choices, indicating that it is likely that b equals `2. if b=2,` then a must be a for the numerator to equal 11. Test this by pugging the numbers into the equation:
`(3(3) +2)/(2) =11/2`
Thus, ` a/b=3/2,` conffirmig (A) as the answer. You ca avoid a lot of work by using key information in the answer choices to pick numbers.