Python을 사용하여 수학 혼합 문제 풀기

혼합물에 대한 수학 문제를 발견했고 Python과 플롯을 사용하여 솔루션을 설명하는 방법에 대해 생각하고 있었습니다. 문제는:

기름과 물이 혼합된 20갤런의 탱크가 제공됩니다. 기름의 비율은 40%입니다. 조성물을 25% 오일로 희석하기 위해 물을 첨가하였다.
a) 희석된 혼합물의 총 중량은 얼마인가?
b) 물을 얼마나 넣었습니까?

문제를 해결하기 위해 먼저 알려진 것을 적어 봅시다.

import numpy as np
import matplotlib.pyplot as plt

orig_mix_weight = 20       # 20 gallons of original mixture
orig_mix_oil_per = 0.4     # percentage of oil in the original mixture
diluted_mix_oil_per = 0.25 # percentage of oil in the diluted mixture

# percentage of water in the original mixture
orig_mix_water_per = 1 - orig_mix_oil_per
orig_mix_water_per
0.6

water, oil = 10, 9  # Assume 10 represents water and 9 oil in the matrix

# create an array with water and oil as elements in the proportion
orig_mix = np.random.choice([water, oil],
                           size=(orig_mix_weight,),
                           p=[orig_mix_water_per, orig_mix_oil_per]) # probability
orig_mix = orig_mix.reshape(5, 4) # make it a 5x4 matrix for visualization
orig_mix

      
                

                    
                    
                
            

[m,n] = np.shape(orig_mix)

plt.figure()
plt.imshow(orig_mix, alpha=0.8, cmap='Reds')
plt.xticks(np.arange(n))
plt.yticks(np.arange(m))
plt.title('Original Solution')
plt.show()

      
                

                    
                    
                
            

orig_mix_oil_weight = orig_mix_weight * orig_mix_oil_per
orig_mix_oil_weight # weight of oil in original mixture
8.0
diluted_mix_oil_weight = orig_mix_oil_weight
diluted_mix_oil_weight # weight of oil in diluted mixture
8.0

diluted_mix_alcohol_per = 0.25
diluted_mix_weight = 1 / diluted_mix_oil_per * diluted_mix_oil_weight
diluted_mix_weight
32.0

diluted_mix_water_per = 1- diluted_mix_alcohol_per

diluted_mix = np.random.choice([water, oil],
                           size=(int(diluted_mix_weight),),
                               p=[diluted_mix_water_per, diluted_mix_alcohol_per])
diluted_mix = diluted_mix.reshape(8, 4) # make it a 5x4 matrix for visualization

[m,n] = np.shape(diluted_mix)

plt.figure()
plt.imshow(diluted_mix, alpha=0.8, cmap='Reds')
plt.xticks(np.arange(n))
plt.yticks(np.arange(m))
plt.title('Diluted Solution')
plt.show()

      
                

                    
                    
                
            

diluted_mix_weight - orig_mix_weight
12.0