Question

The sum of two numbers is 22. Three times one number increased by five is 35.

b) What are the two numbers? Response area and Response area

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's call the two numbers x and y.

The first sentence gives us the equation:
x + y = 22

The second sentence gives us the equation:
3x + 5 = 35

To solve this system of equations, we can first solve the second equation for x:
3x = 35 - 5
3x = 30
x = 30/3
x = 10

Now we can substitute the value of x into the first equation to solve for y:
10 + y = 22
y = 22 - 10
y = 12

So, the two numbers are 10 and 12.

Answer 2

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

Let's solve the problem step-by-step.

Step 1: Define the variables.
Let's assume the two numbers as "x" and "y".

Step 2: Write the given information as equations.
The sum of two numbers is 22. This can be written as:
x + y = 22 ----- Equation 1

Three times one number increased by five is 35. This can be written as:
3x + 5 = 35 ----- Equation 2

Step 3: Solve the equations simultaneously.
We can solve the equations using the method of substitution or elimination.

Using the method of substitution:
From Equation 1, we can express "y" in terms of "x":
y = 22 - x ----- Equation 3

Now we can substitute the value of "y" from Equation 3 into Equation 2:
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 30/3
x = 10

Substituting the value of "x" back into Equation 1 to find "y":
10 + y = 22
y = 22 - 10
y = 12

So, the two numbers are 10 and 12.

Answer 3

[AI-generated answer — Explain Bot]

To find the two numbers, let's use algebra to set up a system of equations based on the given information.

Let's assume that the two numbers are x and y.

From the first statement, "The sum of two numbers is 22," we can write the equation:
x + y = 22 (Equation 1)

From the second statement, "Three times one number increased by five is 35," we can write the equation:
3x + 5 = 35 (Equation 2)

Now, let's solve this system of equations using either substitution or elimination method:

Substitution method:
1. Solve Equation 1 for x: x = 22 - y
2. Substitute the value of x in Equation 2:
3(22 - y) + 5 = 35
Distribute 3: 66 - 3y + 5 = 35
Combine like terms: -3y + 71 = 35
Subtract 71 from both sides: -3y = -36
Divide both sides by -3: y = 12
3. Substitute the value of y into Equation 1:
x + 12 = 22
Subtract 12 from both sides: x = 10

Therefore, the two numbers are x = 10 and y = 12.