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

Question

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

kindly show your solution

Answer 1

Let's assume that the number of vanilla cones sold on Friday was V, and the number of chocolate cones sold was C.

According to the given information, the ratio of vanilla cones sold to chocolate cones sold was initially 2:3. This can be represented as:

V/C = 2/3 Equation 1

If the store had sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3:4. This can be represented as:

(V + 4) / C = 3/4 Equation 2

Now, let's solve this system of equations:

From Equation 1, we can rewrite it as:

4V = 2C Equation 3

By simplifying Equation 2:

4(V + 4) = 3C
4V + 16 = 3C
4V = 3C - 16 Equation 4

Equating Equation 3 and Equation 4, we have:

2C = 3C - 16
16 = C

Therefore, the number of chocolate cones sold on Friday was 16.

Now, substitute the value of C in Equation 3:

4V = 2(16)
4V = 32
V = 8

Thus, the number of vanilla cones sold on Friday was 8.

Answer 2

To solve this problem, let's break it down step by step:

1. Given that the ratio of vanilla cones to chocolate cones sold on Friday was 2:3.

2. Let's assume the number of vanilla cones sold is 2x and the number of chocolate cones sold is 3x. This assumption is based on the ratio given (2:3) where we assign a variable (x) to represent the common multiplier.

3. Now, if 4 more vanilla cones were sold, the new ratio would be 3:4. That means the new number of vanilla cones sold would be (2x + 4) and the new number of chocolate cones sold would be (3x).

4. Set up an equation using the new ratio:
(2x + 4) / (3x) = 3/4.

5. Cross-multiply to eliminate the fraction:
4(2x + 4) = 3(3x).

6. Simplify and solve the equation:
8x + 16 = 9x.

7. Subtract 8x from both sides:
16 = 9x - 8x.

8. Simplify further:
16 = x.

9. Now, substitute the value of x back into the original assumption to find the number of vanilla cones sold on Friday:
Number of vanilla cones = 2x = 2 * 16 = 32.

Therefore, the store sold 32 vanilla cones on Friday.

Answer 3

V/C = 2/3, so C = 3V/2

(V+4)/C = 3/4

V+4 = (3/4)C = (9/8)V
V/8 = 4
V = 32
C = 48