In a video game, Brian collects unbreakable gems, each of which He earns 21 points when he collects 2 red gems and 3 yellow gems. He earns 31 ponts when he collects 2 yellow gems and 3 blue gems, He earns 23 points when he collects 2 blue gems and 3 red gems .When brian collects 2 red gems, 2 yellow gems and 2 blue gems how many points did brian earn?
Answers
Answer:
If the number of points Brian earns when he collects 2 red gems and 3 yellow gems is 21 and the number of points he earns when he collects 2 yellow gems and 3 blue gems are 31 and the number of points he earns when he collects 2 blue gems and 3 red gems is 23, then the number of points he earns when he collects 2red gems 2 yellow gems and 2 blue gems is 30 points
Step-by-step explanation:
Let Ler R, Y, and B be the points for red, yellow, and blue gems respectively
Given
Points Brian earns when he collects 2 red gems and 3 yellow gems = 21
That is,
2R+3Y =21
2R=21-3Y
Points he earns when he collects 2 yellow gems and 3 blue gems = 31
That is,
2Y+3B = 31
2Y= 31-3B
Points he earns when he collects 2 blue gems and 3 red gems = 23
That is,
2B+3R = 23
2B= 23-3R
We have to find
2R+2Y+2B
2R+2Y+2B = 21-3Y+31-3B + 23-3R
5R+5Y+5B = 75
R+Y+B = 75/5 = 15
So, 2(R+Y+B) = 15*2 = 30
Therefore, The number of points he earns when he collects 2red gems 2 yellow gems, and 2 blue gems is 30 points