Final answer:
To obtain the desired ratio of RBC's to WBC's in the new blood sample, the samples from places A and B should be mixed in the ratio of 55:9 to 21:25.
Step-by-step explanation:
To find the ratio in which the two blood samples from places A and B should be mixed to obtain a new sample with RBC's to WBC's in the ratio 4:7, we can use the concept of a weighted average.
Let's assign variables to represent the quantities of RBC's and WBC's in the two samples: R1 represents the RBC's in sample A, R2 represents the RBC's in sample B, W1 represents the WBC's in sample A, and W2 represents the WBC's in sample B.
We are given that the ratio of RBC's to WBC's in sample A is 5:3, which means R1/W1 = 5/3. Similarly, the ratio of RBC's to WBC's in sample B is 3:5, which means R2/W2 = 3/5.
To find the ratio in which the samples should be mixed, we need to find the values of R1 and R2 that satisfy the given ratio of 4:7 in the new sample. For every 4 units of RBC's, there should be 7 units of WBC's. So, we can set up the equation R1+R2/W1+W2 = 4/7.
Using the given ratios, we can substitute R1/W1 = 5/3 and R2/W2 = 3/5 into the equation and solve for the ratio of the samples to be mixed.
By solving the equation, we obtain the ratio R1:R2 = 55:9 and W1:W2 = 21:25. Therefore, the samples should be mixed in the ratio of 55:9 to 21:25 to achieve the desired RBC's to WBC's ratio of 4:7 in the new sample.