The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On friday, the ratio of vanilla cones sold to

[BTGmoderatorDC]

The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On friday, the ratio of vanilla cones sold to chocolate cones sold was 2 to 3. If the store had sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. How many vanilla cones did the store sell on Friday?

A) 32
B) 35
C) 42
D) 48
E) 54


OA A

Source: Princeton Review

[swerve]

The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On friday, the ratio of vanilla cones sold to chocolate cones sold was 2 to 3. If the store had sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. How many vanilla cones did the store sell on Friday?

A) 32
B) 35
C) 42
D) 48
E) 54


OA A

Source: Princeton Review

Given, \(\dfrac{v}{c} = \dfrac{2}{3} \Longrightarrow c= \dfrac{3v}{2}\)

and \(v+\dfrac{4}{c}= \dfrac{3}{4}\)

So, \(4v+16=\dfrac{9v}{2} \Longrightarrow v= 32\)

[Scott@TargetTestPrep]

The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On friday, the ratio of vanilla cones sold to chocolate cones sold was 2 to 3. If the store had sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. How many vanilla cones did the store sell on Friday?

A) 32
B) 35
C) 42
D) 48
E) 54


OA A

Solution:

We can create the ratio:

vanilla : chocolate = 2x : 3x

Had the store sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. So we can create the equation:

(2x + 4)/3x = 3/4

4(2x + 4) = 9x

8x + 16 = 9x

16 = x

Thus, the store sold 32 vanilla cones on Friday.

Answer: A