first, translate all the words into mathematical equations. so that will be:
2a=b
3b=c
d=3c

the next step is to substitute all the equations we've got. C is equal to 3b (c=3b), and we know that b = 2a. So we can write c= 3b= 3(2a)= 6a.
in other words, we state all the variable in terms of one variable (in my case, I chose variable a cause it's easy)
it will be like this:
b= 2a
c= 3b= 6a
d= 3c= 18a

the final step is to write the quantities (A and B) in terms of variable a and do the math. you'll see that quantity A and B are equal: both final result is 1/2

hope this helps

For the positive integers a, b, c, and d, a is half of b, which is one-third of c. The value of d is three times the value of c.

Quantity A	Quantity B
\(\frac{a+b}{c}\)	\(\frac{a+b+c}{d}\)

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

As per the statement
Let b= 4 so that a= 2 , c = 12 and d=36

Therefore for statement 1 we have=

\(\frac{6}{12} = \frac{1}{2}\)

For statement 2 we have

\(\frac{18}{36} = \frac{1}{2}\)

So option C

Explanation

The following relationships are given: \(a =\frac{b}{2}\), \(b = \frac{c}{3}\) , and d = 3c. Pick one variable and put everything in terms of that variable. For instance, variable a:
b = 2a
c = 3b = 3(2a) = 6a
d = 3c = 3(6a) = 18a

Substitute into the quantities and simplify.

Quantity A: \(\frac{a+b}{c}=\frac{a+2a}{6a}=\frac{1}{2}\)

Quantity B: \(\frac{a+b+c}{d}=\frac{a+2a+6a}{18a}=\frac{1}{2}\).

The two quantities are equal.

Answer : C
Solve both quantities in term of C.

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