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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.

Respuesta :

First we need to get some expressions:
"Four times the number of white marbles" = 4*w
"9 times the number of red marbles" = 9*r
"...exceeded...by 10": So 4*w is 10 more than 9*r or 4*w = 9*r +10
"ratio of blue marbles to red marbles is 3 to 1" : b/r = 3/1
b=3*r
"there is a total of 65 marbles": b+r+w=65
So our system becomes

b = 3*r
65 = b+r+w
4*w = 9*r+10

The first equation allows us to substitute immediately into the second equation so
65 = 4*r+w
however, we can divide the third equation by 4 to get w:
w = (9*r)/4+10/4
This can then be plugged into the second to get:
65 = 4*r+(9*r)/4+10/4 = (16*r)/4 + (9*r)/4+10/4 = (25*r+10)/4
260 = 25*r+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 ;)

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