Question

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 7.

Answer 1

To solve the problem, we set up an equation, (1/3)x = (1/7)(184 - x) + 7. By solving this equation, we find that the two parts of 184 are 69.9 and 114.1.

Step-by-step explanation:

To divide the number 184 into two parts such that one-third of one part exceeds one-seventh of the other part by 7, we can set up an equation. Let the two parts be x and 184 - x. According to the problem, (1/3)x = (1/7)(184 - x) + 7. By solving this equation, we will find the value of x, which is one part, and the other part by subtracting x from 184.

Now, let's solve the equation step-by-step:

1. 
   
3. Multiply both sides by 21 (which is the least common multiple of 3 and 7) to clear the denominators:
   21 * (1/3)x = 21 * [(1/7)(184 - x) + 7]
4. 
   
6. Simplify the equation:
   7x = 3(184 - x) + 147
7. 
   
9. Distribute and combine like terms:
   7x = 552 - 3x + 147
10. 
    
12. Add 3x to both sides:
    10x = 699
13. 
    
15. Divide both sides by 10 to find x:
    x = 69.9

Therefore, the two parts are 69.9 and 184 - 69.9, which equals 114.1.