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[(a/b)+1] / (c/b)
In the expression above, a, b and c are different numbers and each is one of the numbers 2, 3 or 5.
What is the greatest possible value of the expression?

A) 8/3 B) 4 C) 9/2 D) 5 E) 6

Answer :

Answer:

B) 4

Step-by-step explanation:

To find what values of a,b and c should be 2,3 and 5 such that the expression results in the greatest value possible.

We need to first simplify the expression, so that we can easily understand it.

[tex]\dfrac{\dfrac{a}{b}+1}{\dfrac{c}{b}}[/tex]

firstly, just break apart the fractions so we have two separate fractions instead one long fraction.

[tex](\dfrac{a}{b}+1)\div(\dfrac{c}{b})[/tex]

division and multiplication are reciprocal to each other!

[tex](\dfrac{a+b}{b})\times(\dfrac{b}{c})\\[/tex]

finally the b's cancel out, making our problem even simpler.

[tex]\dfrac{a+b}{c}[/tex]

Now, in order to have this expression give the largest possible value, we'll need to have:

  1. the larger values at the numerator i.e (3,5)
  2. smaller values at the denominator i.e (2)

[tex]\dfrac{a+b}{c}[/tex]

[tex]\dfrac{3+5}{2}[/tex]

[tex]\dfrac{8}{2}=4[/tex]

so B) 4 is the right answer!

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