The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?

Question

The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?

Answer 1

r/y = 3/4

(r-3)/(y-6) = 4/5

r=27 y=36

check:
27/36 = 3/4
24/30 = 4/5

Answer 2

The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?

Answer 3

To solve this problem, we can use a system of equations. Let's start by assigning variables to the unknown quantities.

Let "x" represent the number of red jelly beans originally in the dish.
Let "y" represent the number of yellow jelly beans originally in the dish.

According to the given information, we have two pieces of information:

1) The ratio of red to yellow jelly beans is 3:4, or alternatively, x:y = 3:4. This means that there are 3x red jelly beans and 4y yellow jelly beans in the dish.

2) After Greg eats 3 red jelly beans and 6 yellow jelly beans, the new ratio becomes 4:5, or x-3:y-6 = 4:5. This means that there are (x-3) red jelly beans and (y-6) yellow jelly beans left in the dish.

Now we can set up the equations:

Equation 1: x:y = 3:4 (1)
Equation 2: x-3:y-6 = 4:5 (2)

To solve this system of equations, we need to eliminate one of the variables. Let's multiply both sides of Equation 1 by 5 and Equation 2 by 4 to get rid of the fractions:

Equation 1 (multiplied by 5): 5x:5y = 15:20
Equation 2 (multiplied by 4): 4(x-3):4(y-6) = 16:20

Simplifying these equations, we get:

Equation 3: 5x:5y = 15:20 (3)
Equation 4: 4x-12:4y-24 = 16:20 (4)

Now let's equate Equations 3 and 4:

15y = 20x (from Equation 3)
4x - 12 = 16y - 24 (from Equation 4)

Simplifying these equations further, we get:

20x - 15y = 0 (5)
4x - 16y = 12 (6)

Now, we can solve this system of linear equations. There are several methods to solve it, such as substitution or elimination. Let's solve it using the elimination method.

Multiply Equation 5 by 4 and Equation 6 by 20 to make the coefficients of x equal:

80x - 60y = 0 (7)
80x - 320y = 240 (8)

Subtracting Equation 7 from Equation 8, we get:

-260y = 240

Dividing both sides by -260, we have:

y = -240 / -260
y = 24 / 26
y = 12 / 13

Thus, there are initially 12 yellow jelly beans in the dish.