Five times the smallest of three consecutive odd integers is ten more than twice the longest. Find the integers.

The sum of three integers is one hundred twenty three more than the first number. The second number is two more than the first number. the third number is five less than the product of three and the first number. Find the three numbers.

The sum of three consecutive integers is one hundred twenty nine. Find the integers.

The sum of three numbers is forty two. The second number is twice the first number, and the third number is three less than the second number. Find the three numbers.

Five times the smallest of three consecutive odd integers is ten more than twice the longest.

Let the middle integer be x.
then the three odd integers are x-2, x, x+2.

Five times the smallest = 5(x-2)
ten more than twice the longest= 2(x+2)+10

so
5(x-2) = 2(x+2) + 10
5x-10 = 2x+4 + 10
5x-2x = 4 + 10 + 10
3x = 24
x = 8
The three integers are 6,8 and 10.

You can solve the other problems in the same way. If you have difficulties, post what you have done.

To solve these problems, we will use algebraic equations to represent the given information and solve for the unknown integers.

1) Five times the smallest of three consecutive odd integers is ten more than twice the longest. Let's represent the three consecutive odd integers as x, x+2, and x+4 respectively.

According to the problem, we can write the equation: 5x = 2(x+4) + 10

Simplifying this equation, we get: 5x = 2x + 8 + 10
5x - 2x = 18
3x = 18
x = 6

Therefore, the three consecutive odd integers are 6, 8, and 10.

2) The sum of three integers is one hundred twenty three more than the first number. The second number is two more than the first number. The third number is five less than the product of three and the first number. Let's represent the three integers as x, x+2, and 3x-5 respectively.

According to the problem, we can write the equation: x + (x+2) + (3x-5) = x + 123

Simplifying this equation, we get: 5x - 3 = x + 123
5x - x = 123 + 3
4x = 126
x = 31.5

Since the question specifies that the integers are whole numbers, we can conclude that there is no solution to this problem.

3) The sum of three consecutive integers is one hundred twenty nine. Let's represent the three consecutive integers as x, x+1, and x+2 respectively.

According to the problem, we can write the equation: x + (x+1) + (x+2) = 129

Simplifying this equation, we get: 3x + 3 = 129
3x = 129 - 3
3x = 126
x = 42

Therefore, the three consecutive integers are 42, 43, and 44.

4) The sum of three numbers is forty two. The second number is twice the first number, and the third number is three less than the second number. Let's represent the three numbers as x, 2x, and 2x-3 respectively.

According to the problem, we can write the equation: x + 2x + (2x-3) = 42

Simplifying this equation, we get: 5x - 3 = 42
5x = 42 + 3
5x = 45
x = 9

Therefore, the three numbers are 9, 18, and 15.

1. Let's start by assuming the smallest odd integer is x.

The consecutive odd integers would be x, x+2, and x+4.
According to the given information, 5 times the smallest integer is 10 more than twice the largest integer:
5x = 2(x+4) + 10.
Solving this equation, we get x = 6.
So, the three consecutive odd integers are 6, 8, and 10.

2. Let's assume the first number is x.
According to the given information:
The sum of three integers is 123 more than the first number, so the equation is: x + (x + 2) + (x + 4) = x + 123.
The second number is two more than the first number, so the equation is: x + 2 = x + 2.
The third number is five less than the product of three and the first number, so the equation is: x + 4 = 3x - 5.
Solving these equations, we get x = 68.
So, the three numbers are 68, 70, and 199.

3. Let's assume the first integer is x.
According to the given information, the three consecutive integers can be represented as x, x+1, and x+2.
The sum of these three integers is 129, so we have the equation: x + (x + 1) + (x + 2) = 129.
Simplifying, we get 3x + 3 = 129.
Solving this equation, we get x = 42.
So, the three consecutive integers are 42, 43, and 44.

4. Let's assume the first number is x.
According to the given information:
The second number is twice the first number, so the equation is: x + (2x) + (2x - 3) = 42.
The sum of three numbers is 42, so we have the equation: x + 2x + 2x - 3 = 42.
Simplifying, we get 5x - 3 = 42.
Solving this equation, we get x = 9.
So, the three numbers are 9, 18, and 15.