A bag contains 4 blue, 5 green and 3 red marbles. How many green marbles must be added to the bag so that at least 79 percent of the marbles are green?
suppose you add \(x\) green marbles
\(\dfrac{green}{total} = \dfrac{5 + x}{4 + 3 + 5 + x} = \dfrac{5 + x}{12 + x} = 0.79\)
multiply both sides by \(12 + x\)
\(5 + x = 9.48 + 0.79x\)
\(0.21x = 4.48\)
\(x = 21.\overline{3}\)
You need to add at least \(21.\overline{3}\) green marbles, but that doesnt make sense here, since you can't have a fractional amount.
Rounding up, at least \(22\) green marbles must be added
