James is hosting a game show where a contestant has to draw a ball that is one of four colors from a pot. Each day, a ball of a particular color will win. To mix up the possibilities, James decides to keep unequal number of balls for each color. There will be as many black balls as red balls. Green balls and red balls should add up to 10. There should be 10 more blue balls than red balls. A math expert tells James that he should have at least 2,304 possible combinations to provide sufficient difficulty. Identify the values for the number of red balls the pot should have to ensure that James' condition is met.

Question

Dante Hendrix

Mathematics

20 April, 02:14

James is hosting a game show where a contestant has to draw a ball that is one of four colors from a pot. Each day, a ball of a particular color will win. To mix up the possibilities, James decides to keep unequal number of balls for each color. There will be as many black balls as red balls. Green balls and red balls should add up to 10. There should be 10 more blue balls than red balls. A math expert tells James that he should have at least 2,304 possible combinations to provide sufficient difficulty. Identify the values for the number of red balls the pot should have to ensure that James' condition is met.

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Answers (1)

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Mario Lam · Answer 1

Let the number of red, black, green and blue balls be R, B, G, U respectively.

B=R (There are as many black balls as red balls)

G+R=10 so G=10-R (Green balls and red balls should add up to 10)

R+10=U (There should be 10 more blue balls than red balls)

The minimal number of balls is 2, 304 so we have the following inequality:

R+B+G+U≥ 2,304

R + (R) + (10-R) + (R+10) ≥2,304

4R≥2,304

R≥2,304/4=576 so R=576

Answer: 576