Problema Solution
A bag contains some red, blue, yellow, and green marbles. 3/10 of the marbles are red, 2/5 are green, and the rest are blue or yellow. There are twice as many blue marbles as yellow marbles. There are 17 fewer blue marbles than red marbles. How many marbles are there in all
Answer provided by our tutors
let 'x' represent the total amount of marbles, the number of blue or yellow marbles is represented by 'x - (3/10)x - (2/5)x'
x - (3/10)x - (2/5)x = (3x)/10 = 0.3x
so 30% of the marbles are blue or yellow
there are twice as many blue marbles as yellow marbles, so let 'b' represent the number of blue marbles, then 'b/2' represents the number of yellow marbles and we have:
0.3x = b + b/2
the number of red marbles is known to be 0.3x, therefore '0.3x-17' represents the number of blue marbles and we have this equation:
0.3x = (0.3x - 17) + (0.3x-17)/2
solving for 'x' we have x=170
there are 170 marbles in all