a bag contains only a red and blue marbles there are a total of 36 marbles in the back there are five red marbles for every four
blue marbles in the bag a student removes one Blue Marble from the bag the student reasons that there are now 5 red marbles in the bag for every 3 blue marbles since 4-1 equals 3
Let R and B be the number of red and blue marbles respectively.
Then, R+B = 36 R:B = 5:4
Therefore, Ratio of red marbles = 5/9 Ratio of blue marbles = 4/9 This means, R = 5/9*36 = 20 marbles B = 4/9*36 = 16 marbles
If one blue marble is removed from the bag, the new B= 16-1 = 15 blue marbles and the new total of marbles in the bag = 36-1 = 35 marbles. The new ratios are R = 20/35 =4/7 B = 15/35 = 3/7 That is, R:B = 4:3
The reasoning of the student is wrong. When a marble is removed, both the number of blue marbles changes as well as the total of the marbles in the bag. In other words, both the values in the ratio reduce by 1.
Since Person 1 can complete the entire job (100% = 1/1 = 1) in 21 minutes, this person can complete 1/21 of the job per minute. This is Person 1's rate. If x is the amount of time it takes both people together to finish the job, then the amount of work Person 1 does would be (1/21)(x) = x/21.
