Question

The sum of three numbers is 45 one number is 10 more than the second number it is also twice the third number find the numbers

Answer 1

The numbers cannot be uniquely determined with the given information.

Step-by-step explanation:

Let's solve this problem step by step.

Let's assume the second number is 'x'. Since the first number is 10 more than the second number, then the first number can be represented as 'x + 10'.

Since the first number is also twice the third number, the first number can be represented as '2y', where 'y' is the third number.

Now, we can form an equation using the given information: x + (x + 10) + 2y = 45

Simplifying the equation, we get: 2x + 2y + 10 = 45

Further simplifying, we get: 2x + 2y = 35

Dividing both sides of the equation by 2, we get: x + y = 17.5

Now, we have two variables and one equation, which means we have an infinite number of possible solutions. We need more information to determine the actual values of x and y.

Therefore, the numbers cannot be uniquely determined with the given information.

Answer 2

x = 1st number, y = 2nd number, z = 3rd number

x + y + z = 45
x = y + 10......x - 10 = y
x = 3z......1/3x = z

x + x - 10 + 1/3x = 45
2 1/3x - 10 = 45
7/3x = 45 + 10
7/3x = 55
x = 55 / (7/3)
x = 55 * 3/7
x = 165/7

x - 10 = y
165/7 - 10 = y
165/7 - 70/7 = y
95/7 = y


1/3x = z
1/3(165/7) = z
165/21 = z
55/7 = z

check...
x + y + z = 45
165/7 + 95/7 + 55/7 = 45
315/7 = 45
45 = 45 (correct)

so, x = 165/7
y = 95/7
z = 55/7