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# The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.

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Joined: 02 Nov 2016
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The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.  [#permalink]

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14 Feb 2019, 02:13
00:00

Difficulty:

25% (medium)

Question Stats:

82% (01:55) correct 18% (02:30) wrong based on 38 sessions

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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

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Re: The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.  [#permalink]

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14 Feb 2019, 06:06
2
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

Say on Friday, the store sold 2x vanilla cones and 3x chocolate cones.

Given:
$$\frac{2x + 4}{3x} = \frac{3}{4}$$

$$8x + 16 = 9x$$

$$x = 16$$

No of vanilla cones sold on Friday = 2*16 = 32

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Re: The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.  [#permalink]

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15 Feb 2019, 05:32
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

given
v/c = 2/3 ; c= 3v/2
and
v+4/c= 3/4
so
4v+16=9v/2
v= 32
IMO A
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Re: The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.  [#permalink]

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15 Feb 2019, 13:53
We can fix the number of chocolate cones in each ratio.

- The actual ratio of v to c was 8 to 12
- If we increase v by 4, the ratio becomes 9 to 12

So increasing the number in the ratio by 1 corresponds to an actual increase of 4, and so our actual numbers must be 4 times what they are in our ratio: we have 32 vanilla and 48 chocolate cones.
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Re: The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.  [#permalink]

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18 Feb 2019, 19:17
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

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.

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Re: The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate.   [#permalink] 18 Feb 2019, 19:17
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