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?

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

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