Question

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue

Answer 1

(C) $\frac{1}{3}$ fraction of the marbles now in the bag is blue.

What is a fraction?

• A fraction is a portion of a whole or, more broadly, any number of equal parts.
• In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
• A common, vulgar, or simple fraction that consists of a numerator above a line and a non-zero denominator below that line.
• Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.

To find what fraction of the marbles now in the bag is blue:

• Important information is that immediately before the last step blue marbles formed $\frac{1}{5}$ from the marble in the bag.
• That means that there were $x$ blue and $4x$ other marbles, for some $x$.
• When we double the number of blue marbles, there will be $2x$ blue and $4x$ other marbles.
• Hence, blue marbles now form $\frac{1}{3}$ all marbles in the bag.

Therefore, (C) $\frac{1}{3}$ fraction of the marbles now in the bag is blue.

Know more about fractions here:

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Complete question:

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

(A) 1/5

(B) 1/4

(C) 1/3

(D) 2/5

(E) 1/2