Answer:
Let's solve this problem step by step. Let's assume the larger number is **L** and the smaller number is **S**.
According to the given information, we have two equations:
1. The sum of two numbers is 35: **L + S = 35**.
2. The sum of 3 times the larger and 6 times the smaller is 132: **3L + 6S = 132**.
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.
From equation 1, we can express **L** in terms of **S**: **L = 35 - S**.
Substituting this value of **L** into equation 2, we get:
**3(35 - S) + 6S = 132**.
Simplifying the equation:
**105 - 3S + 6S = 132**.
Combining like terms:
**3S = 27**.
Dividing both sides by 3, we find:
**S = 9**.
Now, substituting this value of **S** back into equation 1, we get:
**L + 9 = 35**.
Simplifying the equation:
**L = 26**.
Therefore, the larger number is **26**, and the smaller number is 9
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Explanation: