Write two mixed numbers so that all rules are applied:
1. One number is larger than the other by 4 2/3
2. The difference of the numbers is equal to the smaller number.
3. The sum of the numbers is natural number.
What are the numbers?
M=N+14/3
M-N=N
M+N=natural
M-N=14/3
M-N=N
subtract
0=14/3-N
N=14/3
M=28/3
check: M+N=natural number=42/3=14
To solve this problem, let's break it down step by step:
Step 1: Let's assume the smaller mixed number as x.
Step 2: According to the first rule, the larger mixed number is x + 4 2/3.
Step 3: According to the second rule, the difference between the larger and smaller mixed numbers is equal to the smaller mixed number, so we can set up the equation:
(x + 4 2/3) - x = x
Simplifying the equation, we get:
x + 4 2/3 - x = x
4 2/3 = x
Converting the mixed number to an improper fraction, we get:
4 + (2/3) = (4 * 3/3) + (2/3) = 14/3
Therefore, x is equal to 14/3.
Step 4: Now that we have the value of x, we can find the larger mixed number by adding 4 2/3 to x:
x + 4 2/3 = 14/3 + 4 2/3
Combining the whole numbers and fractions, we get:
14/3 + 4 2/3 = 18/3 + 2/3 = 20/3
Therefore, the larger mixed number is 20/3.
So, the two mixed numbers that satisfy all the given rules are 14/3 and 20/3.