9th grade "extra credit" math problem?

If 16 jelly beans are not red, that’s the total of the green, blue, and yellow ones. And if 16 aren’t green, that’s the total of the red, blue, and yellow ones. Likewise, if 16 aren’t blue, that’s the total of the red, green, and yellow ones. Last, if 18 aren’t yellow, that’s the total of the red, green, and blue jelly beans.

Each color is included three times in the four totals: 1) green, blue, yellow; 2) red, blue, yellow; 3) red, green, yellow; 4) red, green, blue. And the totals add up to 66 (meaning 16+16+16+18=66).

So, three times the number of each color equals 66, which means 22 jelly beans are in the bowl. Looking back at the question, we see that six are red (“all but 16”), six are green, six are blue, and four are yellow.

Let g = the number of green jelly beans

Let r = the number of red jelly beans

Let b = the number of blue jelly beans

Let y = the number of yellow jelly beans

all but 16 are red ==> g + b + y = 16

all but 16 are green ==> r + b + y = 16

all but 16 are blue ==> r + b + y = 16

all but 18 are yellow ==> r + b + y = 18

Now you have four equations with 4 unknowns. Maybe your daughter has learned how to solve systems of linear equations. I used MS Excel and Cramer's Rule I get 4 yellow and 6 each of the other colors.

(I like Marilyn's solution better.)

This was already asked in yahoo answer. I found it by doing a google search for "all but 16 are red". Marilyn's came up as the other link.

Let's say there are x jelly beans in the bowl

there are r red ones, g green ones, b blue ones, and y yellow ones

x = r + y + g + b

x - 16 = r

x - 16 = g

x - 16 = b

x - 18 = y

x = r + y + g + b

x = (x-16) + (x-16) + (x-16) + (x-18)

x = 4x - 66

-3x = -66

x = 22

**edit**

if you want the amount of each color, just put your value of x into the top equation

x - 16 = r

r = 22-16

r = 6

x - 16 = g

g = 22-16

g = 6

x - 16 = b

b = 22-16

b = 6

x - 18 = y

y = 22-18

y = 4

I also realized that the method i used was taught to me in grade 11, i don't know why its being given in grade 9, even for extra credit.

You know:

16 aren't red.

16 aren't green.

16 aren't blue.

16 aren't yellow.

x-16 = r OR x-r = 16

x-16 = g OR x-g = 16

x-16 = b OR x-b = 16

x-18 = y OR x-y-2 = 16

r+g+b+y = x

Set things equal to one another.

x-r = x-g = x-b = x-y-2

-r = -g = -b = -y-2

r = g = b = y+2

Set the variable a to represent r, g, b, and y+2. Substitute into your first equation.

x-r = 16

(r+g+b+y)-r = 16

a+a+a+a-2-a = 16

3a - 2 = 16

3a = 18

a = 6

Now you know:

a = r = g = b = y+2 = 6

Thus, there are 6 red, green and blue marbles each, and 4 yellow marbles.

Let x be the total number of beans.

So:

r=x-16

g=x-16

b=x-16

y-x-18

The total number of beans is the sum of all the colors:

x=(x-16)+(x-16)+(x-16)+(x-18)

x=4x-66

-3x=-66

3x=66

x=22

So, 6 red, 6 green, 6 blue, and 4 yellow.

2 red, 2 green, 2 blue

22 total, 6 red, 6 green, 6 blue, 4 yellow

http://www.parade.com/askmarilyn/archive/Sundays-C...

yep... thats exactly what i was gonna say.