SOLUTION: The ratio of the number of reds to the number of blues was 2 to 1, and 5 times the sum of the number of reds and blues exceeded 3 times the number of whites by 12. If there were 4

Question 67415This question is from textbook Advanced mathematics
: The ratio of the number of reds to the number of blues was 2 to 1, and 5 times the sum of the number of reds and blues exceeded 3 times the number of whites by 12. If there were 4 more whites than blues, how many were red, how many were white, and how many were blue? This question is from textbook Advanced mathematics

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
We will let:
x=number of reds
y=number of whites
z=number of blues

Now we are told the following:
x/z=2/1 cross multiply
x=2z-------------------------our 1st equation
We are also told that:
5(x+z)=3y+12-----------------our 2nd equation
They also tell us:
y=z+4------------------------our 3rd equation
substitute x=2z into our 2nd eq. and we get
5(2z+z)=3y+12
15z=3y+12 Now substitute y=z+4 into this equation:
15z=3(z+4)+12;
15z=3z+12+12 subtract 3z from both sides and collect like terms;
12z=24
z=2 ----------------------------------number of blue balls
substitute z=2 into our 3rd eq.
y=z+4=2+4=6---------------------------number of white balls
substitute z=2 into our 1st eq
x=2z=2*2=4-----------------------------number of red balls
ck
(1) ratio of red balls to blue balls is 2/1; 4/2=2/1 CHECKS
(2) 5 times the sum of the number of reds and blues exceeded 3 times the number of whites by 12. 5*6-12=3*6 or 18=18-------CHECKS
(3) there were 4 more whites than blues 6-2=4 CHECKS

Hope this helps---ptaylor

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