the Average age of three number is 32 base 5.If the sum of two number is 131 base 4.Find the third number in base 6?

Step plz

let's do the math in base 10.

325 = 1710
1314 = 2910

x+y+z = 3*17 = 51
x+y = 29

now you can get z, and convert to base 6.

given that 231n- 143n=44n, find the number base n

Step 1: Convert the average age of the three numbers from base 5 to base 10.

To convert a number from base 5 to base 10, we will multiply each digit by the corresponding power of 5 and sum the products.

The average age in base 5 is 32 base 5.
To convert this to base 10, we calculate:
3 * 5^1 + 2 * 5^0 = 3 * 5 + 2 * 1 = 15 + 2 = 17.

So, the average age in base 10 is 17.

Step 2: Convert the sum of the two numbers from base 4 to base 10.

The sum of the two numbers in base 4 is 131 base 4.
To convert this to base 10, we calculate:
1 * 4^2 + 3 * 4^1 + 1 * 4^0 = 1 * 16 + 3 * 4 + 1 * 1 = 16 + 12 + 1 = 29.

So, the sum of the two numbers in base 10 is 29.

Step 3: Find the third number in base 6.

Let the third number be x in base 6.

We know that the average of the three numbers is 17, and the sum of the two numbers is 29. Therefore, the sum of all three numbers is 17 * 3 = 51.

So, the equation can be written as: x base 6 + 29 = 51.

To solve for x, we can subtract 29 from both sides: x base 6 = 51 - 29 = 22.

Therefore, the third number in base 6 is 22.

To find the solution, follow these steps:

Step 1: Convert the average age (32 base 5) to base 10.

To convert a number from base 5 to base 10, multiply each digit of the number by the corresponding power of the base (5).

32 base 5 = (3 * 5^1) + (2 * 5^0) = 15 + 2 = 17 base 10.

So, the average age in base 10 is 17.

Step 2: Find the sum of the two numbers (131 base 4) in base 10.

To convert a number from base 4 to base 10, multiply each digit of the number by the corresponding power of the base (4).

131 base 4 = (1 * 4^2) + (3 * 4^1) + (1 * 4^0) = 16 + 12 + 1 = 29 base 10.

So, the sum of the two numbers in base 10 is 29.

Step 3: Find the third number in base 6.

Let the third number be x (in base 6).

Since the average age is the sum of all three numbers divided by 3, we can use this equation:

(17 + 29 + x) / 3 = 32 (in base 5) = 17 (in base 10)

(46 + x) / 3 = 17

Multiply both sides by 3 to eliminate the fraction:

46 + x = 51

Subtract 46 from both sides:

x = 5

Therefore, the third number in base 6 is 5.