Question

a bag contains 120 marbles. some are red and the rest are black. there are 19 red marbles for every black marble. how many red marbles are in the bag?

Explanation:

Step1: Define variables

Let the number of black marbles be \( x \). Then the number of red marbles is \( 19x \) (since there are 19 red marbles for every black marble).

Step2: Set up equation

The total number of marbles is the sum of red and black marbles, so \( x + 19x = 120 \).

Step3: Solve for \( x \)

Combine like terms: \( 20x = 120 \). Then divide both sides by 20: \( x=\frac{120}{20}=6 \).

Step4: Find number of red marbles

Since red marbles are \( 19x \), substitute \( x = 6 \): \( 19\times6 = 114 \).

Answer:

114