A container has red blue and white marbles. Four times the number of white marbles exceeded 9 times the number of red marbles by 10. The ratio of blue marbles to red marbles was 3 to 1. There is a total of 65 marbles of all 3 colors. Form a system of equations with variables red marble: r, white marble: w, and blue marble: b. Solve the system of equations to find the number of white, red and blue marbles in the container.
First we need to get some expressions:
"Four times the number of white marbles" = 4w
"9 times the number of red marbles" = 9r
"...exceeded...by 10": So 4w is 10 more than 9r or 4w = 9r +10
"ratio of blue marbles to red marbles is 3 to 1" : b/r = 3/1
b=3r
"there is a total of 65 marbles": b+r+w=65
So our system becomes
b = 3r
65 = b+r+w
4w = 9r+10
The first equation allows us to substitute immediately into the second equation so
65 = 4r+w
however, we can divide the third equation by 4 to get w:
w = (9r)/4+10/4
This can then be plugged into the second to get:
65 = 4r+(9r)/4+10/4 = (16r)/4 + (9r)/4+10/4 = (25r+10)/4
260 = 25r+10
250 = 25*r
r=10
Now we simply plug this result into the substitutions to get w and b:
w = 90/4+10/4 = 100/4 = 25
b=30
So there are 10 red marbles, 25 white marbles, and 30 blue marbles
Now it sounds like we should be picking some out at random ;)