a bag contains 6 red tiles and 15 yellow tiles. remove 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 me
So we are supposed to remove 2 red from the 6 red, and x yellow from the 15 yellow so that
4/(15-x) = 6/15
60 = 90 - 6x
6x = 30
x = 5
check:
the original ratio was 6/15 = 2/5
the new ratio is (6-2)/(15-5) = 4/10 = 2/5
i m so confused with this question
I know right!
The answer is 10
To solve this problem, we need to maintain the ratio of red tiles to yellow tiles as 6:15 when two red tiles are removed from the bag.
Let's start by finding the new number of red tiles in the bag after two are removed. Initially, there are 6 red tiles, so after removing two, there will be 6 - 2 = 4 red tiles left.
Next, we have to determine how many yellow tiles should be removed so that the ratio of red to yellow tiles remains 6:15.
The ratio of red to yellow tiles is currently 4:15 (as there are 4 red and 15 yellow tiles). To maintain the ratio at 6:15, we need to increase the number of red tiles by 2 and the number of yellow tiles by some amount.
The ratio can be expressed as (4 + 2):(15 + x), where x represents the number of yellow tiles to be removed.
Since the ratio of red to yellow tiles should remain the same, the ratio (4 + 2):(15 + x) should be equal to 6:15. Hence, we can set up the following equation:
(4 + 2)/(15 + x) = 6/15
Now, we can solve for x:
(6)/(15) = (4 + 2)/(15 + x)
6(15 + x) = 15(4 + 2)
90 + 6x = 90
6x = 0
x = 0
According to the calculations, no yellow tiles need to be removed to maintain the ratio of 6:15 after removing 2 red tiles.