The ratio of red jelly beans to yellow jelly beans in a dish is 3.4. If Greg eats 3 red ones and 6 yellow ones, the ratio is 4.5. How many yellow jelly beans were originally in the dish?
Do you make 3.4 a fraction and 4.5 a fraction and times them? 3/6 TIMES 4.5 = 12/20 THEN SUBTRACT 6 yellow ones?
Ratios are written 3:4, not 3.4
Initially,
r/y = 3/4
Later,
(r-3)/(y-6) = 4/5
Solve those two equations to get
r=27, y=36
To solve this problem, we can set up a proportion using the given information.
Let's define the number of red jelly beans as "x" and the number of yellow jelly beans as "y".
According to the given ratio, the first equation we can set up is:
x/y = 3/4
Now, based on the second scenario where Greg eats 3 red jelly beans and 6 yellow jelly beans, we need to update the ratio.
Since Greg's actions affect the total number of beans, we need to adjust the ratio accordingly. The new equation becomes:
(x-3) / (y-6) = 4/5
Now we have a system of equations:
x/y = 3/4
(x-3) / (y-6) = 4/5
To solve this system, we can use the method of substitution. We solve the first equation for x:
x = (3/4)y
Now substitute this value of x in the second equation:
((3/4)y - 3) / (y - 6) = 4/5
Multiply both sides of the equation by (y - 6) to eliminate the denominator:
((3/4)y - 3) * 5 = 4(y - 6)
Now solve for y:
(15/4)y - 15 = 4y - 24
Move all the terms containing y to one side:
(15/4)y - 4y = -24 + 15
Combine like terms:
y * (15/4 - 4) = -9
Multiply:
(15/4 - 16/4)y = -9
(-1/4)y = -9
Now isolate y by multiplying both sides by -4:
y = (-9) * (-4/1)
y = 36
So, there were originally 36 yellow jelly beans in the dish.