Question

twice the number of reds exceeded three times The number of blues by 8. The ratio of the reds the the sum of the reds and blues was 5 to 7. How many were red and how many were blue?

Answer 1

2r=8+3b
r/(r+b)=5/7
cool problem bro

so first
2r=8+3b
divide both sides by 2
r=4+1.5b
sub 4+1.5b foor r

(4+1.5b)/(4+1.5b+b)=5/7
(4+1.5b)/(4+2.5b)=5/7
times (7)(4+2.5) to both sides (cross multiply)
7(4+1.5b)=5(4+2.5b)
distribute
28+10.5b=20+12.5b
minus 10.5b both sides
28=20+2b
minus 20 both sides
8=2b
divide by 2
4=b

sub back

r=4+1.5b
r=4+1.5(4)
r=4+6
r=10


10 red
4 blue

Answer 2

we have :
2r = 3b + 8 ==> 2r - 3b = 8 (1) and r / (r + b) = 5/7 ==> 7r = 5r + 5b ==> 2r - 5b = 0 (2) therefore (1) - (2) gives -3b - (-5b) = 8 - 0 ==> 2b = 8 ==> b = 4
2r - 5b = 0 (2) ==> r = 5/2 * b = 5/2 * 4 = 10
reds = 10 blues = 4