Question

the sum of two numbers is 22 and three times one number is increased by five is 35

what are the two numbers

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's represent the two numbers as x and y.

We are given two pieces of information:

1) The sum of the two numbers is 22:
x + y = 22

2) Three times one number is increased by five and it equals 35:
3x + 5 = 35

From equation 1, we can rewrite it as x = 22 - y.

Substituting this value of x into equation 2, we get:
3(22 - y) + 5 = 35

Simplifying this equation:
66 - 3y + 5 = 35
71 - 3y = 35
-3y = 35 - 71
-3y = -36

Dividing both sides of the equation by -3:
y = -36 / -3
y = 12

Now, substitute this value of y back into equation 1:
x + 12 = 22
x = 22 - 12
x = 10

Therefore, the two numbers are 10 and 12.

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's solve this problem step by step:

Step 1: Let's assume the first number as 'x' and the second number as 'y'.

Step 2: According to the given problem, the sum of two numbers is 22. This can be expressed as:

x + y = 22 ----(Equation 1)

Step 3: The problem also states that three times one number is increased by five is 35. This can be expressed as:

3x + 5 = 35 ----(Equation 2)

Step 4: Now we have two equations:

x + y = 22 ----(Equation 1)
3x + 5 = 35 ----(Equation 2)

Step 5: Let's solve Equation 2 for x:

3x + 5 = 35

Subtract 5 from both sides:

3x = 35 - 5
3x = 30

Divide both sides by 3:

x = 30/3
x = 10

Step 6: Now that we have the value of x, let's substitute it into Equation 1 to find y:

x + y = 22

Substituting x = 10:

10 + y = 22

Subtract 10 from both sides:

y = 22 - 10
y = 12

Step 7: So, the two numbers are 10 and 12.

Therefore, the two numbers are 10 and 12.

Answer 3

[AI-generated answer — Explain Bot]

To find the two numbers, we can set up a system of equations based on the given information.

Let's say the two numbers are x and y.

From the first piece of information, "the sum of two numbers is 22," we can write the equation:
x + y = 22

From the second piece of information, "three times one number is increased by five is 35," we can write the equation:
3x + 5 = 35

Let's solve this system of equations to find the values of x and y.

First, let's simplify the second equation:
3x + 5 = 35
Subtract 5 from both sides:
3x = 30
Divide both sides by 3:
x = 10

Now we have the value of x. We can substitute this value into the first equation to solve for y:
10 + y = 22
Subtract 10 from both sides:
y = 12

Therefore, the two numbers are 10 and 12.