Question

a bag contains 6 red tiles and 15 yellow tiles. lila removes 2 red tiles. how many yellow tiles should she remove so that the ratio of red tiles to yellow tiles in the bag stays equivalent to 6 : 15? show your work.

Explanation:

Step 1: Find the new number of red tiles

Original red tiles: 6. Remove 2, so new red tiles: \(6 - 2 = 4\)

Step 2: Set up the proportion for the ratio

Let \(y\) be the number of yellow tiles left. The ratio of red to yellow should stay \(6:15\), so \(\frac{4}{y}=\frac{6}{15}\)

Step 3: Solve for \(y\)

Cross - multiply: \(6y = 4\times15\)
\(6y = 60\)
Divide both sides by 6: \(y=\frac{60}{6}=10\)

Step 4: Find the number of yellow tiles to remove

Original yellow tiles: 15. New yellow tiles: 10. So tiles to remove: \(15 - 10 = 5\)

Answer:

Lila should remove 5 yellow tiles.